Well, I'm a little reticient to give the ones I have come up with so far, because I don't want to the guy who comes up with something stupidly wrong (or worse--offensive), but here's what I've currently got:
American Indian: Wakonda Pantheon
Aztec: Tamoanchan Pantheon
Babylonian: Ilyas
Celtic: Tuatha De Dannan
Indian: Brahmanic Pantheon
Japanese: Ama-Tsu-Kami
Sumerian: Annunaki
Egyptian: Ennead
I stick with 3e's Asgardians and Olympians for the Norse and Greek (when possible, I use terms that don't require sticking "Pantheon" on the end of it).
With the Olympians, Egyptians, and Sumerians (and there might have been others) where the name technically refers to a subset of their deities, I figured that the name is associated strongly enough with their pantheons' identities, that the fact that it only refers to a sub set of big names amongst them probably shouldn't disqualify it as a general term. Adherents of a religion probably care about these subtleties. Someone rattling off a list of names of pantheons in the multiverse probably doesn't.
I also have always like the Celestial Bureaucracy, so that's an easy pick for me. It's both interesting and annoying that the Celestial Bureaucracy they made for Kara-Tur isn't the same as the one they made for Legends & Lore (which is what Planescape uses). I think I went through both versions and compared the deities and decided that most of them could be different names for the same person, and the few that didn't fit well were just gods that weren't as universally known.
Looks like I forgot to come up with anything for Finnish as of yet.
I'm happier with some than with others. In particular, I don't like "Brahmanic Pantheon" because it's not very accurate for the particular pantheon presented.
I really want the Sumerian pantheon to be the Annunaki, so I'm tentatively going with that, even though the way they did the Sumerians and Babylonians means they actually gave Anu to the Babylonians and not the Sumerians, so I really should give the name to the Babylonians. But I didn't. There's probably some way I can spin it so makes sense (at least to the Annunaki themselves).
One thing I tried when I couldn't come up with anything satisfying was to just find the equivalent of "the gods" in their language, hence the Babylonian "Ilyas".