I haven't said Saul didn't persecute Christians but when he became the new creation Paul he didn't.
Try think it through.
I want to elaborate on more of personal level as to why it is important to me to get it out there that Paul was still called Saul sometimes even after he was saved. See sometime after I was saved, it was a little of a concern to me on whether I should have people call me a different name now, because well Paul had a name change, right? It wasn't a real big struggle for me or anything, but something a baby Christian might wonder about. I think people should know and accept the truth when they hear it so they can keep moving on in knowing God better. Paul was a man who was violent and changing his 'S' to a 'P' was probably not to have people gasp when they heard the name 'Saul'. Another thing to consider is how it is wrong to think we need another name, and it is something the Catholic denomination teaches to do. In other countries in the past, the parents picked another name when the baby was baptized, it became like a middle name. In America, the Catholic denomination teaches to get another name at the time of confirmation, and they really stress to pick a name of a "Catholic Saint".
So I hope now you understand more of the passion behind my posts to you about Paul and his name and how we aren't told to do that.