Usernames cannot be changed and that is understandable, for they are your ID on Spotify. And since there are surely many people with the same whole names, your selected username makes you unique and distinguishable on this platform.
However, my problem has been that my friends (or even myself) cannot find me by typing in my display name in the search bar. I'm connected to Facebook, so my display name is naturally brought from there. I find this highly inconvenient, because I'd like to be found by everyone who has ever personally known me. I can only find my profile by typing in my personal selected username, and that's sad because no one else but me knows it. Spotify is a great place to find new music, because I for one have found many new cool songs by searching with my dance instructor, new work colleague and past childhood friend's (with whom I'm more or less lost connection through the years) whole names. And I'd like for those people who know me by name to be able to find my profile and public playlists, too, just by typing in my display name in the search bar. Sure enough, the search might come up with several results, because people have same first and surnames, but if you know me, you find the right profile by looking at the profile picture.
I don't know if I'm the only one with this problem, but here's my idea in a nutshell:
Make a tab in the privacy settings, which allows you to either be or not be found by typing in your display name in the search bar. With the unique username, anyone can be found, but that is only if you know someone's super secret unpredictable username. With the display name privacy tag, you can choose if you want your profile to be found with your display name, which might be your full name if you're connected to Facebook, so that it's visible in the search results. Or you can turn the tab off, so even if you're connected to Facebook and your display name is your full name, your profile won't show up in the search results just by typing in your display name, but then someone'd be required to know your personal username.