PlayStation Network has been around for over 11 years now, and plenty its 70 million active user accounts that have been around for that long. Unlike Xbox Live, PSN usernames are unchangeable. Once you make the account, that's it, you're stuck with it, and there's plenty of people stuck with an account username that seemed a lot wittier a decade ago when they were in middle and high school.
The permanency of PSN usernames wouldn't be such a big deal, but with digital downloads becoming more and more prevalent, it's not rare to find people with hundreds and thousands of dollars of games from the PlayStation store attached to their PSN username. Eleven years is a long time, and it can be embarrassing for someone in their late-20s or early 30s to have an unfortunate username like "T34MJ4C0B," "MySpace-B0SS." or "BillCosbysSweater." Fortunately, Sony may be addressing this soon.
Changing your PSN name has been one of the most asked for features since the PS3 debuted, and it seemed like Sony was just going to leave fans hanging. In 2014, President and CEO of Sony Interactive Entertainment America Shawn Layden said that part of the reason your PSN handle is permanent is to prevent griefing in games, which made it seem like the matter was cut and dry on Sony's end. In 2015, technical reasons were cited as the problem. However, In a recent interview with GameSpot at PlayStation Experience Layden said that he hoped the feature would be implemented by PSX 2018.
Layden went on to say that the ability to change your name on PSN is "more complex than you think" from a technical standpoint. On the Xbox, you've been able to change your name for a long time, with the first change being free and subsequent ones costing a small amount of money. If name changing on PSN is implemented, we'll probably see a similar system since it seems to have worked out for Microsoft.