Does anybody know what the name of this game might be?
Yes, yes I do. The game you're thinking of is Agent USA. The C64 version (I didn't play the others) had a particularly catchy song, which is currently my ringtone. It's been in my head that long.
Edit: You can get the Atari version of this song (naturally, not as good as the C64 version) here.
"One word of warning: if you meet a bunch of Perl programmers on the bus or something, don't look them in the eye. They've been known to try to convert the young into Perl monks." - Frank Willison