Basically what happened

Yeah basically.

There was Simon the Zealot and then Simon, called Peter.

Actually he renamed him that because it means "the rock" much like Peter and his faith.

True story: When my friend's grandparents got together, the grandpa was called Simon. Grandma didn't like this name, and preferred peter, her EX-BOYFRIEND'S name. She insisted he change it 3 months into the relationship. For some reason, he did, and to this day they are still together and he is still called peter.