To change your PSN name now, you would already have to be part of a special PlayStation beta program.
The PlayStation Preview Program beta is accessible only to players that have previously signed up for it. If you want to change your PSN name when the feature goes live in 2019, there are some caveats.
To change your PSN name, it currently is free to do so for the first time. This is likely to entice those in the PlayStation Preview Program to test out the new feature. However, when beta testers want to change their name a second time, it costs them $10 to do so ($5 for PlayStation Plus members).
Why you would want to change your PSN name so many times is beyond me. It seems as though Sony has thought about this some, as no matter how many times you do end up changing your PSN name, you can choose to have your original tag displayed in parenthesis next to your new tag.
The beta testers are lucky, because if past precedent is anything to follow, Sony won’t be handing out free passes to change your PSN name again. It’s a highly requested feature, meaning that Sony can easily charge the reasonable prices listed above to allow users to do so.
Lastly, when you change your PSN name, it will work with all games released past April 1, 2018, but will only work with “the majority of the most-played PS4 games” from before that date. That’s a bit of a vague way of putting things, but it’s understandable, as not every single game publisher is going to want to have to make an update in their game’s code to allow the PSN name changes.