Biblical name changes are important.
God changed Abram's name to Abraham:
God changed Sarai's name to Sarah:
God changed Jacob's name to Israel:
Paul also had a name change:
That's the story of Saul's name being changed to 'Paul.' No divine being told him to change his name. There was no reason given for his name change. It was changed out of season. If there was a time to change Paul's name, it would have been during the Damascus experience, when Paul claims Jesus (or Ananias, if he is in the mood to credit him) gave him the mission to go to the Gentile. Not weeks (or years, if you believe his three-year stint in Arabia occurred) after.
In fact, if we dig deeper into history, we find that Paul did not change his name. Paul was a Roman citizen of Tarsus.
As a Roman citizen,(Acts 22:27, 28.) he was required to have a Roman name. His Roman name, from birth, was Paul. His Jewish name, from birth, was Saul.
Saul switched his name to his other name, to make him seem important, just like Abram, Sarai, and Jacob. But the truth is his name change was not a name change, was not given by God, and there was no legitimate reason for it.
Value of this Evidence
This is excellent evidence against Paul's character, which is decent evidence against Paul being a true apostle. We would expect the apostles to be as exemplary as Jesus was, since Jesus was the Way. But since Paul is sly, even with his name, his claim to apostleship becomes weaker.