Baby Jesus stories were late additions to early christian lore

[Bucky Ball]

They also claimed he changed his name from Saul to Paul, (which in Latin means "small").

"Paulus" sometimes spelled with two "Ls" was an almost exclusive cognomen of the Aemilian clan.  They were an ancient Roman patrician family - Lucius Aemilius Paulus got himself killed as consul at the Battle of Cannae and the family remained prominent down to the reign of Augustus.  One does wonder why they would go all the way to Palestine to add some smelly jew to their ranks?

Or, is that just more bullshit?

Originally the story is that his name was Saul of Tarsus. I didn't know about the noble Roman family "Paulus". 
If in fact he was related to them, the family in Tarsus would have gone by that name, and there would have been more made of the fact that a noble Roman "sat at the feet of Gamaliel" https://en.wikipedia.org/wiki/Gamaliel

Yeah no. It's all bullshit.