Welcome to the PlayStation Community Forum.
Your name is permanent. You may create new user names, but nothing tied to your current PSN ID will be able to be transferred, i.e. trophies, DLC, progress in games, etc.
As well, your name here remains you PSN ID that you choose. It cannot be changed or altered here either.
Just the way it is. Feel free to read the PSN User Agreement, if you have any further questions, or ask one of us. We will try to help with anything.