Well...maybe it's not exactly that simple. The names don't mean exactly the same thing. First, many think that Paul derives from the Latin Paulus. In Latin, the name means "small." But actually Paul's use of the name probably derived from the Greek Paulos, which means "at rest" or "one who is at rest (or at peace)." Saul means "prayed for." So while the two names are from Hebrew/Aramaic (Saul) and Greek (Paul), they are not simply the same name in different languages.
My guess is that Saul took on the name Paul as he went to the Gentiles because of a compilation of reasons: (1) the name Saul was distinctly Hebrew/Aramaic, and he didn't want that to define him, (2) the name Paul sounded a lot like Saul, and (3) the dramatic change of his conversion did transform him from someone who needed to be "prayed for" to someone who was "at peace (rest)."
So, then, more than Luke swapping names because one was used while he was dealing with the Jerusalem church and the other as Paul went to the Gentiles, it is actually Paul himself who probably thought up and instituted the name change.