At the moment, it’s not possible to change your profile or display name in the app.
If you want a profile that displays a new name, you can always create a new accountthrough your email address. We've made this Spotify Answer on how you can start over with a new account to help with that.
During the sign up you will get to create a profile name that’s displayed in the app. You can enter your preferred display name in the "What should we call you?" field. This is how other Spotify users can search for you in the app and it will show on your profile, app, playlists, and Friend Activity.
While there's no limit when selecting your profile name, once your account is created, you won't be able to change it.
If you choose to create a new account and you have the student discount, you won’t be able to apply it to your new account until 12 months have elapsed since you signed up for it. There's more info here.
If your account was created through Facebook and your profile name turned into numbers there's a different Spotify Answer that you can check instead.
Keep in mind that if this is something you'd like to be able to do in the app, you can also consider adding your +VOTEto this idea. The Community team is actively bringing your feedback to the internal teams at Spotify - check how here.