Were the islands/countries discovered by Hispanic explorers named after Mozarabic feast days?

You don't specify which discoveries are of interest, but the specific days on which islands were encountered is definitely recorded in ships' log books. For example, a log survives of Magellan and Elcano's voyage and was published on Cambridge University Press as "A Log-Book of Magellan's Voyage, 1519–1522". Cross-referencing it with feast calendars would answer your question. Another source of detailed information on Spanish place naming are journals from terrestrial expeditions like that of Juan Bautista de Anza. Not all the place names established were Catholic, of course.

First, the Mozarabic Rite was also Catholic, the correct terms would be Mozarabic versus Roman Rites. I have heard a Mozarabic Mass (and I keep the printed missal), and (personal opinion) I did not consider it sufficiently different (it was developed with strong influences from Roman traditions anyway) to justify keeping it alive with a separated calendar and all jurisdictional and practical issues that arise from a separate Rite. To my layman hears it sounded mostly the same mass with similar but changed texts, and some parts appearing in different order.

Eastern Rites (Catholic and Orthodox) have much more differences in rites and customs, independently developed traditions and a patriarchal hierarchy: they are not just a local variation on the Roman Rite and customs.

And, at the discoveries time, the Mozarabic rite was not widely practised.

About place names: There are places named after saints during the first Portuguese voyages through Brazil coast that correspond to the Roman calendar of saints. As we know that they traveled from North to South, and the place names follow the order of saints in the calendar from N to S, it is even possible to count the number of days they took to go from one place to the other by checking how many days there were between the corresponding Saints in the Roman Calendar. Besides that, there are letters and diaries from that voyages that use the Roman Calendar to name saints days.

If you read portuguese you can check the many books written 20 ys ago to commemorate the 500y of Brazil discovery - the most popular ones were from Eduardo Bueno.

Another evidence: the first ecclesiastical jurisdiction to cover Brazil was Tomar parish church connected to the Order of Christ (both Roman rite) [source: stone inscription at that church]. Not much latter, Brazil was transferred to Lisbon diocese (also roman rite) until Brazil got his own (roman) bishop. I do not see any lapse of time were a Mozarabic jurisdiction was existing.

Besides that it would be easy for a captain to find an unemployed roman rite priest in XVI c. Portugal to hire as a ship chaplain if needed.

EDIT about the comment about unemployed priests (not related to the answer)

In some places, e.g., city of Porto, there are churches called "Clergyman's Church" (Igreja dos Clérigos). But every church is not under some clergyman? What is that? Then you learn that this church cared about poor clergymen. But if he is a priest, does not he have a job?

This is true today, as there are so few priests that no bishop would let a priest jobless. Now I give info from a book written in Coimbra to commemorate the 500y of the College of the Jesuits, with essays to explain local life in 1550. I don't remember the title, but it was a local commemorative publication with essays from different authors. The college was founded in 1548, so it was probably published around 1950

In Coimbra, in an specific single year around 1550, the seminar graduated around 50 people. With philosophy and theology licentiatures, they had the academic requirements to be ordained. But the diocese only had jobs for 9 of them, and got to choose the 9 best students.

What did the ~40 others do? To be ordained, academic degrees were not enough, one had to have an income. And if the bishop did not have an available job to provide such income, the graduated seminarian could only be ordained if he could find an income for himself. Obviously, all of this supposes that his superiors consider him worthy of priesthood.

Some found jobs as chaplains in hospitals, army, large farms, etc. Some could look for jobs in other dioceses, and could ask the bishop to be incardinated in other diocese (which could also have surplus of priests, so it might be easy or not). Some gave up and were not ordained. They still could find secular work as clerks or administrative positions. Some could seek membership in religious orders.

And a common charity work was to give money to poor seminarians to allow them to be ordained. e.g., an old woman died and left a small farm or house to a seminarian. The seminarian rents his real state, and with this income, the bishop allows him to be ordained. He would not have regular diocesan work, but he could be paid to say mass in private homes, find temporary or odd jobs as chaplain of something, help with festive High Masses when more priests are required, or just wander around and try to help people, etc.

There were a requirement for a minimum income which would allow the priest to live (very poorly though) if he finds no other income or falls ill. And, this kind of income brings risks. What if the small farm bankrupts, or the rented house burns down? What if he does not receive rents for some reason? What if the priest gets really ill and needs to pay medics? This is the raison d'etre for "Clergyman's Church": to look after these destitute priests.

So, a captain looking for a chaplain in 1550 would be literally a godsend for many poor priests or senior seminarians.

When I read this I was also surprised. It is so different from today's mindset or situation. "Priest surplus" today sounds like "square circle". The bishop requiring that a priest candidate provides for himself is also strange, today we think that even mother state should feed us everything, even more mother church. But it does make sense. How could every ship have a chaplain? How could every rich guy have private masses at home if he so wished, or ask for extra masses for his deceased relatives? Why so many lateral altars in churches, who would use them if there were only a few priests in the parish? How could so many priests find time to be scientists or politicians? How could a bishop spare a priest to be a missionary to a 100-person tribe? Today these "jobs" would be unthinkable - we have a priest to tens of thousands of people. If you think how the life of a under-employed priest should be hard (in terms of staying busy and resisting temptations), this also explain why there were so many half-crazed eccentric priests, priests with children, destitute priests, etc, and again, why there were so many "Igreja dos Clérigos" to look after these guys.

Also, at Coimbra there were only Law, Medicine, Canons, and Theology. Not many options to study. Besides that, Coimbra was the ONLY university in Portugal. Every smart guy wanted to study there. I do not expect that every local diocesan seminar would have such 80% priest surplus, but I have never seen other hardcore precise data.

Were the islands/countries discovered by Hispanic explorers named after Mozarabic feast days?

The short answer is no.

But that no has to be clarified. It could be yes or no, according to which Rite the person who named the said lands belonged to. Both Rites were in use in Spain at the time of the Spanish colonization of the Americas.

The name "Mozarabic Rite" is given to the rite used generally in Spain and in what afterwards became Portugal from the earliest times of which we have any information down to the latter part of the eleventh century, and still surviving in the Capilla Muzárabe in Toledo cathedral and in the chapel of San Salvador or Talavera, in the old cathedral of Salamanca. The name is not a good one. It originated in the fact that, after its abolition in Christian Spain, the rite continued to be used by the Christians in the Moorish dominions who were known as Mazárabes or Muzárabes. The form Mostárabes is also found. The derivation of the word is not quite certain, but the best theory seems to be that it is musta’rab, the participle of the tenth form of the verb ’araba, and that it means a naturalized Arab or one who has adopted Arab customs or nationality, an Arabized person. Some, with less probability, have made it a Latin or Spanish compound, Mixto-Arabic. The meanings, which are not far apart, applied entirely to the persons who used the rite in its later period, and not to the rite itself, which has no sign of any Arab influence. The names Gothic, Toledan, Isidorian, have also been applied to the rite—the first referring to its development during the time of the Visigothic kingdom of Spain, the second to the metropolitan city which was its headquarters, and the third to the idea that it owed, if not its existence, at any rate a considerable revision. - Mozarabic Rite (Catholic Encyclopædia)

It should be noted that none of explorers of the 15th or 16th centuries were sent from the Archdiocese of Braga, Portugal. Braga also had it’s own liturgical Rite within the Church.

The Rite of Braga (or Bragan Rite) is a Catholic liturgical rite associated with the Archdiocese of Braga in Portugal.

The Rite of Braga belongs to the Roman family of liturgical rites and took shape within the Archdiocese of Braga between the 11th and 13th centuries.[1] The Missal of Mateus, which dates to the second quarter of the twelfth century, is the oldest known source for this Rite. It was more than 200 years old at the time of Pope Pius V's papal bulls Quod a nobis of 9 July 1568 and Quo primum of 14 July 1570. The rite was unaffected by the imposition of the Roman Rite throughout the Latin Church. This was due to the exception made for regions where another rite had been in use for at least two centuries. However, the Roman Rite was increasingly adopted within the archdiocese and non-traditional elements were admitted into celebrations of the archdiocese's rite.

In the 20th century an attempt was made by Archbishop Manuel Vieira de Matos, with the approval of Pope Pius XI, to expunge these accretions, to revise the texts and to make the rite obligatory within the archdiocese. After the Second Vatican Council the priests of the archdiocese, while authorized to use the Rite of Braga, have in general opted to use the Roman Rite. The Rite of Braga

The Mozarabic Rite, also called the Visigothic Rite or the Hispanic Rite, is a liturgical rite of the Latin Church once used generally in the Iberian Peninsula (Hispania), in what is now Spain and Portugal. Thus we can call it a liturgical variation of the Extraordinary Form of the Mass.

Since the liturgical reform of Pope St. Paul VI, the Mozarabic Rite has almost completely disappeared within Spain. The Mass according to this liturgical Rite can still be found in Spain if one looks hard enough.

Here is the real conundrum with this question. The feast days of the Tridentine Roman Rite and the Mozarabic Rite for the most part followed the same liturgical calendar with a few minor exceptions. In this sense the naming of the lands discovered in the 15th and 16th centuries could be literally named according to either liturgical Rite. It would all depend on which Rite the person who named the islands belonged to. It is sure that both Rites were in use in Spain at the time.

It should be noted the Spain has (and did have) some local feasts not celebrated in other countries and this also applies (and did apply) to both liturgical Rites.

As I have already stated above that the true answer to this question will depend on which Rite the person of authority belonged to. As it happens, both Queen Isabella of Spain and Christopher Columbus were of the Roman Rite.

Christopher Columbus in fact was Italian and that says volumes to this subject matter:

Christopher Columbus [(before 31 October 1451 – 20 May 1506) was an Italian explorer, navigator, and colonist who completed four voyages across the Atlantic Ocean under the auspices of the Catholic Monarchs of Castile and Aragon. He led the first European expeditions to the Caribbean, Central America, and South America, initiating the permanent European colonization of the Americas. Columbus discovered a viable sailing route to the Americas, a continent that was then unknown to the Old World. While what he thought he had discovered was a route to the Far East, he is credited with the opening of the Americas for conquest and settlement by Europeans. - Christopher Columbus (Wikipedia)

The Catholic Encyclopedia further states that in Queen Isabella’s day the Roman Rite prevailed and that she allowed the Mozarabic Rite to be used within the Spanish Kingdom:

When Ferdinand and Isabella took Granada in 1492, there were certainly some Mozarabic Christians there, as well as Christian merchants and prisoners from non-Moorish countries, but whether the Mozarabic Rite was used by them does not appear. With the discouragement which began with Alfonso VI came the period of decadence. The civil privileges (fueros) of the Toledo Mozárabes, which, though in 1147 Pope Eugene III had definitely put them under the jurisdiction of the bishop of the diocese, included a certain amount of independence, were confirmed by Alfonso VII in 1118, by Peter in 1350, by Henry II in 1379, and by Ferdinand and Isabella in 1480 (later also by Philip II in 1564, by Charles II in 1699, and by Philip V in 1740). But in spite of this the "Roman Rite prevailed so much that it was introduced even into Mozarabic churches, which only used the old rite for certain special days, and that in a corrupted form from old and imperfectly understood manuscripts This and the dying out of many Mozarabic families gradually brought the rite very low. - Rite (Catholic Encyclopedia)

Ferdinand Magellan was also of the Roman Rite for although Portuguese; he was of minor nobility and thus not of Muzarabic descent.