Today, there are few services that do not allow you to change usernames, PSN is one of them. But now it will change accordning to the rumors.
Sony insider Tidux writes on Twitter:
Good News! looks like PSN namechange is closing in! bad news? looks like you have to give up content prior to the PS4 if you wanna change you PSN name. Trophies, games and saves. i´m not 100 on the last point. #PS4 #PS4Pro #PS3 #PSN
— Tidux (@Tidux) September 24, 2018