geofft is likely right, and it doesn't seem to be a particularly controversial topic amongst different strains of Christianity topic at that. (I've seen conservative and more liberal sources that think Saul/Paul was a sort of dual name.) The most concrete verse on the matter seems to be Acts 13:9:

  > But Saul, who was also known as Paul, filled with the Holy Spirit, fixed his gaze on him

That's not to say that name changes are never indicative of internal change in the Bible, and it's possible that Saul started using the name Paul more intentionally to represent his change. But there doesn't seem to be much concrete evidence of that.