Here are a few suggestions made by members of the Community:
@Jude /@user-removed suggest asking your friend to send you a link to one of their playlists. When you open the link to the playlist, you will find a link to their profile.
@David suggests typing 'spotify:user:[username]' into the search bar on the desktop or mobile app.
Note: if your friend doesn't know their username, they can easily find it by doing the following:
If you want to change your username, make sure to check out this thread to find out how.
Hope that helps!