The text indicates he had two names, a Roman name, Paul, and a Hebrew name, Saul. His letters and Acts were written in Greek, so naturally Paul is the name used. There is nothing in the text to suggest he abandoned his Hebrew name.It's more than merely possible. You're right that the text doesn't say that, but you're wrong to say that we have no reason to think he did. He only ever calls himself Paul in the letters we have from him (interestingly, his imitators also only ever use the name). This doesn't prove that he changed his name, but it's certainly a reason to suppose he did.
As far as I am aware, Paul considered himself a Jew even after becoming a follower of Jesus. Why would he give up his Hebrew name?