You don't have to notate if you play it into Noteworthy Composer on a keyboard. When I get a tune like that, I usually try to record it on a small portable tape player first, then work on it from there. That way I know I won't forget it.:-) You can also sing it or play into Real Producer and take it into Notate It! if you want sheet music.

As for what do you call it? In orchestra we called it "playing second fiddle!" That usually meant no melody part, just harmonising, etc. as the others have noted.