We aren’t told why Paul’s name changed from Saul to Paul (we aren’t actually even told that it was Paul who changed his own name, although it’s a fair guess that he did). The verse that mentions the change of name is Acts 13:9:
But Saul, who was also called Paul, filled with the Holy Spirit, looked intently at him
Although we aren’t told why Paul’s name was changed, here is a possibility:
Saul was also the name of the first human king of Israel (God was the first king: 1Sam. 8:7); that Saul was very tall (1Sam. 9:2) and he also became a very bad king (1Sam. 15). King Saul was a good king when he was ‘small in his own eyes’ (1Sam. 15:17) — i.e. when he was a humble person. When he became proud he became a wicked king.
In contrast, Paul means little or small — perhaps Paul’s name was changed because once he had been a bad person, proud (Phil. 3:4-6), like king Saul, but now he was a Christian trying to be humble (Phil. 3:7-11).
#1 by Rob J Hyndman on February 2nd, 2010
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It’s possible that he always had two names — Saul being his Jewish name and Paul his Roman name. This was quite common, especially for someone who was both Jewish and a Roman citizen. His apparent change of preference to use Paul rather than Saul may also have been to help in his efforts to preach to non-Jews.
#2 by Grahame Grieve on August 10th, 2010
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David Rohl proposes that Saul himself had a name change, that his original name was “Lebayu” (though everything proposed by Rohl is controversial)