Jesus did not change Saul’s name to Paul.
Some believe that Paul was just the Roman/Latin equivalent of Saul, but the Bible gives us no explanation as to why two different names are used.
Maybe I am misreading your post.
I did not say Jesus changed Saul’s name to Paul.
I think Saul is his Hebrew name, while Paul is his Latin name which he uses for Gentiles in the Roman Empire.
Paul is from the Roman family name Paulus, which meant “small” or “humble” in Latin.
Saul on the other hand is from the Hebrew name Sha’ul which meant “asked for” or “prayed for”.