During the preview program, you will be able to change your online ID as many times as you want. The first change is free, and changes after that will cost $9.99 USD / CAD. For PlayStation Plus members, it will cost $4.99 USD/ CAD after the first change. Changes to online ID can be made through the Settings menu or via the Profile page of your PS4.
Mine has never been the most terrible one, but it is still a nickname that I haven't used in years, so I'm definitely going to change mine.