The parallel story in Mark 2:14-22 and Luke 5:27-38 agree Jesus called Levi the to leave his tax booth and follow him. Virtually every detail is the same except the name and the citation of Hosea 6:6. Why does Matthew 9:9 have Matthew and not Levi?
The name Matthew is Μαθθαῖος (or Ματθαῖος) in Aramaic it is either מתי or מתא. The name is likely an abbreviation of Mattaniah or Mattithiah (2 Kgs 24:17; Neh 8:4) which means “gift of Yahweh.” The name Matthew is therefore not related to the Greek noun translated disciple (μαθητής). Mark calls Levi “the son of Alphaeus” complicating this issue since in Matthew 10:3, Matthew is “the tax collector” and James is the “the son of Alphaeus.” Luke 5:27 has Levi but not Alphaeus, perhaps to avoid confusion (Dulling, 619). If this was not confusing enough, there are a variety of textual variants which try to sort out the problem.
I agree with Hagner (WBC, 238) that is most likely Matthew and Levi are the same person. Like Joseph the Levite who was also called Barnabas (Acts 4:36), Matthew may have had two names (France, Matthew, 352). There are a number of people in the New Testament with two names; Simon bar Jonah is also called Cephas (on Aramaic) or Peter (in Greek). Some scholars suggest Levi was his pre-conversion name. After following Jesus, he was known as Matthew (similar to Saul/Paul in Acts; Hagner, Matthew, 238; Turner, Matthew, 12)
If Matthew is indeed the author of the first Gospel, then this he made this editorial change himself. The main problem with this view is there is no name-change story, either canonical or non-canonical.
There are several other less-likely suggestions. First, Levi may not be a name, Albright and Mann suggested Matthew was a Levite (Albright and Mann, Matthew, clxxviii). Second, some suggest there were two different tax collectors called by Jesus, the author of the fourth Gospel used the name “Matthew” since that was the name he knew (Davies and Allison, Matthew, 99). Third, the use of Matthew in 9:9 is the author’s self-identification. Fourth, the author of the first gospel may have replaced Levi with Matthew for theological reasons.
Regardless of whether the name is Levi or Matthew, when Jesus calls the tax collector as a disciple, he demonstrates the kind of mercy God requires. This stands in contrast to the Pharisees, who question Jesus when he eats with “sinners” (9:10-13) and the disciples of John who wonder why Jesus is eating at all (9:14-17).
Bibliography: Dennis C. Duling, “Matthew (Disciple),” ed. David Noel Freedman, The Anchor Bible Dictionary (New York: Doubleday, 1992), 619; J. G. Bashaw, “Matthew the Apostle,” ed. John D. Barry et al., The Lexham Bible Dictionary (Bellingham, WA: Lexham Press, 2016).