I also like both Zealots and Fundamentalists for the Advent, but I think that Fundamentalists would go better with the Loyalists because they are keeping to the Advent fundamentals, whereas the Zealots could go for both sub-factions, and so I think it is a little less awesome. I also hear the word "zealots" a lot more than the word "fundamentalists", so I think that it is a bit too overused to be a sub-faction name.
Great suggestions though.
Well the reason "Apostates" is so great for the Rebels is because they're pretty much a textbook definition of Apostates.
"(apostates) Members who seriously oppose or ignore cardinal teachings of the Church, publicly or privately."
The Rebels have basically become a splinter "religion" in direct opposition to the Loyalist teaching that their "destiny" is that they destroy the TEC and conquer the Universe, assimilating or destroying everything in their path.
Fundamentalist works because, well, yeah, they're just fervently sticking with the same old song with renewed vigor and rejecting any other possibility (like peace.)
I do hope StarClad read this thread, I think this (subtle) change would make the faction split a bit more interesting.
And speaking of which, how about changing the default acronym that the TEC Rebels get on their Capital Ships/Titans? "TDN" stood for "Trader Defense Network", which fits perfectly with the Loyalists, but not so much with the new militant "xenophobic lynch mob" that is the Rebels.