NoYes, since April 10, 2019, you can now change your PSN name.
First, it'sbe aware that you can only possibledo so once for free. After that, each change will cost you $5/£4 if you're a PS Plus subscriber or $10/£8 if you're not. You can also call support to change back to any of your displayprevious names for free however.
Changing your name in Japanis also only guaranteed to work for games published since April 1, 2018. OtherwiseMost older games, you'llPS3 games, and Vita games will have to make a new PSN account. If you doissues, and you can keepmight lose game progress or DLC. Here is a good video going over some of the issues, but to summarize some examples: Little Big Planet and Call of Duty 4: Modern Warfare surprisingly work fine with the same email addressnew name, by changingGrand Theft Auto 4 and Modern Warfare 2 treat it before making theas a new PSN account, but there's no wayand Black Ops 2 completely fails to keepload if you're signed in and can irreversibly corrupt your trophies or online statsPS3's hard drive if your try signing in with the game running. So, uh, yeah, be careful.
Support LinkNow on to how to do it, as taken from Sony's help article:
Change Your Online ID from Your PlayStation®4
Step 1: From your PS4 go to [Settings].
Step 2: Select [Account Management] > [Account Information] > [Profile] > [Online ID].
Step 3: Enter your new online ID.
Step 4: Follow the on-screen prompts to complete the change.
Once you complete the change process, you are signed out from all your devices.Change Your Online ID from a Web Browser
Step 1: Sign in to PlayStation™ Network Account Management and select PSN Profile in the menu.
Step 2: Click Edit button next to your current online ID.
Step 3: Enter your new online ID.
Step 4: Follow the on-screen prompts to complete the change.
Once you complete the change process, you are signed out from all your devices.
Any further questions can probably be answered by http://us.playstation.com/support/answer/index.htm?a_id=254Sony's FAQ on the subject.