My first name has two words, and after connecting my Facebook profile with Spotify, it seems to only parse the first two words in a name, which means my last name doesn't show up in Spotify. This makes it hard for friends to search for my profile.
That's odd. Have you tried re-entering your name on your Facebook account? Is it a double-barreled name (i.e. Mary-Jane, Billy-Bob) and is it quite long?
No, it's just one word followed by a space, followed by another. It's not too long--only 9 characters including the space.