You will not be able to change your PSN username on the PS4. Hopefully you like the one you have already on your PS3 or Vita. You've asked us this before. And we've asked them. Sorry. Ain't happening. Sony confirmed this today in their massive PS4 FAQ.
Is there a way to rename my Online ID on PS4?
No. But PS4 does give you the option of allowing your friends to see your real name in addition to your Online ID. You can also choose to import your Facebook photo to be used as your PSN profile picture if you wish.
They do make a good point about supporting use of real names as a supplemental option. That's cool (for some of us!).
Microsoft has long allowed people to change their Gamertags. They charge $9.99 for the name change. Presumably they will continue to offer that.
Suggestion to Sony: maybe offer this in a firmware update?