So it dawned on me that there IS a way to do this...sort of....
I will caution that you’re going to lose all your trophy information (Sorry folks) and that this is not a real “name change” so to speak.
1. First up make a PSN account with your desired screen name.
2. Sign out of your primary account on your PS4.
3. Click “Add user” and sign into your new PSN account.
4. That’s it!
Since you are using the same PS4 as your primary account you’ll have access to any game that your primary account does which means you won’t lose your games. You’ll only lose your trophy information. However, this can be a good way to start to transition away from xXNo_scrote_blaz_itXx to something a little more respectable.
I realize this is kind of ....dumb. However, for me it is a way for me to finally not have the screen name of my ex wife’s last name mashed with mine. (ugh. what was I thinking.)