He didn’t change his name to Paul after his conversion experience on the road to Damascus
He was born a Jew with a Roman citizenship inherited from his father, & thus carried both a Hebrew & a Latin name since his birth.
He used “Saul” (שָׁאוּל,) in Jewish contexts & “Paul” (Paulus) as an international missionary
Acts 13:9 :
“…Saul, who also is called Paul…”