I don't know anything about him or his decision to change from Paul to Saul, but Paul/Saul is on of the most important Christian apostles. As both Jew and Roman citizen, his Jewish name was Saul (from the Jewish king Saul in the Old Testament maybe?) and his Roman name was Paul. So just changing the first letter might not be completely random. :-)

https://en.wikipedia.org/wiki/Paul_the_Apostle#Names