the gospel of Mark and Luke refer to the tax collector among the 12 as Levi while the first (canonical) gospel calls him Matthew.  How to account for the discrepancy?

Some scholars justify assigning both names to one disciple by noting that Jews in this period sometimes bore two names, one Greek and another Semitic.  To the best of my knowledge, Neither Matthew nor Levi are Greek; both are Semitic, and there is little evidence of Semitic persons during this period possessing two Semitic names.

E.P. Sanders intriguingly suggests that some of the names in the lists may differ because membership fluctuated: disciples may have died, or abandoned the mission.  For Jesus and his movement the need for 12 mattered more than who constituted the 12.

I propose an alternative solution; the names Matthew and Levi both refer to a single member of Jesus’s core of disciples, but only one of the names (Levi) was natural, the other (Matthew) was a nickname later acquired (perhaps during his time with Jesus).  Here is the evidence:

In Matthew the tax collector is introduced to us as “one who is called Matthew”.  The gospel of Matthew has already used this phrasing with regard to Peter, “Simon, who is called Peter.” That is, Matthew uses the phrase “is called” of Peter’s NICKNAME.  Mark does not say Levi was “called Levi”.  He was simply Levi.  So then we have the following:

In Mark, we are introduced to Simon/Peter by his birth name, Simon, and only later told that he was given the nickname Peter.  Mark introduces us to the tax collector simply as Levi.

In Matthew, we are introduced to Simon/Peter immediately as “Simon, who is called Peter”; that is, Matthew gives us his birth name and then indicates his nickname with “is called”.  Then, when introducing us to the tax collector, also uses the same phrase, “is called”.  

Thesis: the tax collector’s name was Levi, but at some point in his life he acquired the nickname (i.e., was called) Matthew.