Once the update goes live to the PlayStation Preview Program, you will be able to change your online ID through either the Settings menu or Profile page of your PS4. However, only users who've registered for previous system software betas will be eligible.
During the preview program, users will be able to change their online ID multiple times.
You will be able to display your old username alongside your new ID in order for friends to recognise you online. This is a choice users will have to make; once you decide to display your old ID or not, you won't be able to change this. Sony's giving you the first change free, but after that you'll have to fork out $9.99; PlayStation Plus members will pay slightly less at $4.99. Numerous most popular PS4 games that were released prior to that date will work as well, but beware, several games will not have the PSN ID change function.
Your first ID change will be free of charge, allowing you to erase any embarrassing usernames you may still have. "For PlayStation Plus members, it will cost $4.99". This preview program will end in November 2018. It does warn that not all games and applications for PS4, PS3, and PS Vita will support the change and you may encounter some issues using them with a new ID. The service has grown exponentially since then, but in all of that time one much-asked-for feature has eluded subscribers: name changes. We'll get a list of officially compatible games at some point in the future.
KitGuru Says: I've been wanting to change my name for quite some time after my online moniker was inexplicably denied. If you're not in the Preview Program, the feature will not be available until Sony gives it an official full release.
If you are not one of the lucky test users, you will need to wait until 2019, when a full roll out is planned for the feature.