Is Levi from Luke 5:27 and Mark 2:14 referring to the apostle Matthew

Mark, the first New Testament gospel to be written, mentions both Levi and Matthew separately, referring to Levi, son of Alphaeus, as a tax collector whom Jesus called to follow him (Mark 2:14). So, we can identify Levi from two facts, that his father was called Alphaeus and that he was a tax collector (publican). As in Mark 2:14, Luke 5:27 also says Levi rose and followed Jesus, but he is never again mentioned in either gospel. The two gospels introduce the twelve disciples (Mark 3:14-19; Luke 6:14-16), including Matthew, Thaddaeus, and James, son of Alphaeus, but there is no mention of Levi. These lists do have a son of Alphaeus, although this disciple's name is James, but they do not have a tax collector (publican).

Matthew first appears in both gospels in the full list of disciples (Mark 3:18; Luke 6:15), but neither gospel says he was a tax collector, or that he was the son of Alphaeus and therefore brother of James, son of Alphaeus. Mark sets a precedent by describing another James and John as brothers, and Luke follows suit also mentioning Simon and Andrew as brothers in the same list, making the failure to mention that Matthew and (the second) James were brothers a puzzling omission if that were the case. The conclusion to be drawn at this stage is that Matthew was not the son of Alphaeus, although we know Levi was, so one possibility is that he changed his mind after first following Jesus.

Disciples are not meant to change their minds when called by Jesus, an issue that the author of Matthew recognises and then creates a solution. The anonymous author resolves Levi's unexplained absence among the disciples simply by not mentioning Levi at all, and by having Matthew as the disciple who was a tax collector, in the parallel account at Matthew 9:9, then including him as "Matthew the publican" in the list of disciples at Matthew 10:3. What Matthew fails to do is portray Matthew as the son of Alphaeus, or the brother of James the son of Alphaeus. The only possible reason for Matthew's portrayal of Matthew as a tax collector is one of apologetics, to resolve the continuing absence of Levi, but I believe this is unconvincing. Either Matthew was the son of Alphaeus and brother of James or he was not, and Matthew's author does not suggest that when you could expect him to have done so. Almost two thousand years of tradition have followed Matthew in holding that Levi and Matthew must be the same person, but this happens only in Matthew's Gospel, not in either Luke or Mark.

It is highly unlikely that Matthew and Levi were the same person.
Richard Bauckham goes into more detail on this in his book "Jesus and the Eyewitnesses" but I will summarize it. It is true that a lot of people had two names in this historical context, but they were usually used for two reasons:

1. Having a Greek/Latin name next to a Semitic name
2. A person having an uncommon nickname next to his common name to differentiate himself from the other people with the same name.

"Levi" and "Matthew" are both very common Semitic names. It practically never happened elsewhere that a person bore two common Semitic names and it wouldn't make much sense because it wouldn't distinguish the person in any way.

Even if "Matthew" is a semitic name, it doesn't negate the possibility of name changing. The name changing from a semitic name to another one is not unusual. We recognize the name changing of Abram to Abraham and Simon to Cepha. Why not Levi to Matthew (Mattija? = Gift of Yahweh)?

Moreover, the fact that the name Levi was mentioned only once in the story of his calling, and never again, it doesn't necessarily means he quit. A lot of names were mentioned only once in the Scripture, and among them, Jesus' disciples. To name a few: Joseph of Arimathaea, Simon and the other disciple from the Emmaus journey, most of the deacons. Even the three siblings: Martha, Mary and Lazarus only appear in the gospels.

It's more likely Matthew and Levi were different disciples than the same. A number of the disciples had other names like we do today, however, the Gospels refer to James the son of Alphaeus (Mark 3:18) as a different disciple from Matthew (Mark 3:18). The Bible also mentions a disciple : "Levi the son of Alphaeus" (Mark 2:14). It's more likely this James and Levi are the same person rather than Matthew and Levi.

Recall, the Gospels also mention "Simon the Caananite" as well as "Simon Zealotes". It is from the different lists of the twelve that we know they are the same person.

So I believe that there were two "receivers of the custom" amongst the disciples because Levi the son of Alphaeus is also mentioned as sitting at the "receipt of the custom" (Mark 2:14).