I am not familiar with the scientific discussion, but I've done some research. I haven't been able to find any evidence, that
Saul actually changed his name to
Paul. The bible simply states, that
Saul was "also known als
Paul". This is found in Acts 13,9, four chapters after
Paul's conversion and from then on he is referred to as
Paul only. But this does not neccessarily be connected with his conversion. As far as Jewish naming practice is concerned, I found that both was possible: parents giving their children a Jewish name plus a non-Jewish name and adults chosing a non-Jewish name in addition to their given name. Inthe case of
Paul it looks like we simply don't know. Or do you have any additional information?