If your account wasn't created via Facebook, Spotify could take a few days to update the fact that your Facebook is no longer linked to your account. Just to be on the safe side, make sure you're following these steps to remove the link between Spotify and Facebook.
The account should stop showing your name, and revert to the username or account name you chose.
Let me know how it goes.
“Music acts like a magic key, to which the most tightly closed heart opens.” ― Maria Augusta von Trapp