In my experience, you don't need to ask. Your final destination is the one you end up at, regardless of where you connect. I guess, if there is a fare break (ie xxx-yyy is covered under one fare and yyy-zzz is under another), there MAY be a chance that someone goofs up and only checks your luggage to yyy. But from my experiences, you're going to zzz, and that's where your luggage should show up.

Can't hurt to ask at check-in though, just to make sure that they have it going to the right place.