When was the number of the beast, 666, first identified as referring to Emperor Nero?

The first time Nero is directly interpreted as 666 or 616 was in 1831.

The riddle seems to have been forgotten almost as soon as it was written and not solved until 1831 (when it first was proposed), seemingly because the number was assumed to be Greek or Latin—and not a Hebraic one.

http://penelope.uchicago.edu/~grout/encyclopaedia_romana/gladiators/nero.html

About 270 Victorinus mentions Nero in his commentary on Revelation chapter 17, but when it comes to 666 he says the following.

18. “His number is the name of a man, and his number is Six hundred threescore and six.”] As they have it reckoned from the Greek characters, they thus find it among many to be τειταν, for τειταν has this number, which the Gentiles call Sol and Phœbus; and it is reckoned in Greek thus: τ three hundred, ε five, ι ten, τ three hundred, α one, ν fifty,—which taken together become six hundred and sixty-six. For as far as belongs to the Greek letters, they fill up this number and name; which name if you wish to turn into Latin, it is understood by the antiphrase DICLUX, which letters are reckoned in this manner: since D figures five hundred, I one, C a hundred, L fifty, V five, X ten,—which by the reckoning up of the letters makes similarly six hundred and sixty-six, that is, what in Greek gives τειταν, to wit, what in Latin is called DICLUX; by which name, expressed by antiphrases, we understand Antichrist, who, although he be cut off from the supernal light, and deprived thereof, yet transforms himself into an angel of light, daring to call himself light.2304 Moreover, we find in a certain Greek codex αντεμος, which letters being reckoned up, you will find to give the number as above: α one, ν fifty, τ three hundred, ε five, μ forty, ο seventy, ς two hundred,—which together makes six hundred and sixty-six, according to the Greeks. Moreover, there is another name in Gothic of him, which will be evident of itself, that is, γενσήρικος, which in the same way you will reckon in Greek letters: γ three, ε five, ν fifty, σ two hundred, η eight, ρ a hundred, ι ten, κ twenty, ο seventy, ς also two hundred, which, as has been said above, make six hundred and sixty-six.

Irenaeus (130-202) discusses 666 and 616 in chapters XXIX and XXX of Against the Heresies Book V, but he never mentions Nero. Here is an excerpt.

3. It is therefore more certain, and less hazardous, to await the fulfilment of the prophecy, than to be making surmises, and casting about for any names that may present themselves, inasmuch as many names can be found possessing the number mentioned; and the same question will, after all, remain unsolved. For if there are many names found possessing this number, it will be asked which among them shall the coming man bear. It is not through a want of names containing the number of that name that I say this, but on account of the fear of God, and zeal for the truth: for the name Evanthas (ΕΥΑΝΘΑΣ) contains the required number, but I make no allegation regarding it. Then also Lateinos (ΛΑΤΕΙΝΟΣ) has the number six hundred and sixty-six; and it is a very probable [solution], this being the name of the last kingdom [of the four seen by Daniel]. For the Latins are they who at present bear rule: I will not, however, make any boast over this [coincidence]. Teitan too, (ΤΕΙΤΑΝ, the first syllable being written with the two Greek vowels ε and ι, among all the names which are found among us, is rather worthy of credit. For it has in itself the predicted number, and is composed of six letters, each syllable containing three letters; and [the word itself] is ancient, and removed from ordinary use; for among our kings we find none bearing this name Titan, nor have any of the idols which are worshipped in public among the Greeks and barbarians this appellation. Among many persons, too, this name is accounted divine, so that even the sun is termed “Titan” by those who do now possess [the rule]. This word, too, contains a certain outward appearance of vengeance, and of one inflicting merited punishment because he (Antichrist) pretends that he vindicates the oppressed. And besides this, it is an ancient name, one worthy of credit, of royal dignity, and still further, a name belonging to a tyrant. Inasmuch, then, as this name “Titan” has so much to recommend it, there is a strong degree of probability, that from among the many [names suggested], we infer, that perchance he who is to come shall be called “Titan.” We will not, however, incur the risk of pronouncing positively as to the name of Antichrist; for if it were necessary that his name should be distinctly revealed in this present time, it would have been announced by him who beheld the apocalyptic vision. For that was seen no very long time since, but almost in our day, towards the end of Domitian’s reign.