Hello SaintRoseWorld,
Welcome to Apple Support Communities. We understand you're wanting to change the username for your Apple Music account, and we'd like to help.
Go to the Listen Now tab in the Music app. Then, in the upper-right corner, tap your photo icon. At the top of the next screen, tap [your name] View Profile. From there, tap Edit under your current username. You can then edit your Name and Username in Apple Music on that following page, and customize your profile further.
These steps are discussed further within this article: See what friends are listening to in Apple Music on your iPhone, iPad, iPod touch, or Android device - Apple Support
We hope this information is useful. Kind regards.