Another cool topic to ponder, 137th Gebirg! I LOVE IT.
If you go off of the same setup as Star Trek then the first Battlestar of the Jupiter Class should have been named the Jupiter. For the Colonial setup and use of names - that just seems out-of-place/odd. Jupiter is to unique to Earth histroy and our names - not so much the Colonial "other world" differences the show held fast to (i.e. Yarhens instead of Years). They wanted the Colonials to be clearly different than humans on Earth.
Plus to be named Jupiter would clash bad with the Jupiter 2 of Lost In Space. I think producers would try to avoid it. That would be like me making a sci-fi show and calling my ship the Enterprise 2 (same lame rip-off as it were, and very confusing
).
Unfortunately I don't think there is a official canonical source for a classic BSG Battlestar class name. It just was never mentioned in the show... and I view ONLY what is in the broadcast shows to truly be classic BSG canon. Do you all think the same way?
What is canon? 
I think a Battlestar class will always fall into the extended universe realm.
Maybe BSG season two would have fleshed out such details. *cries* We'll never know. 
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As for the Enterprise / Constitution Class, I found this fun bit of info:
(Source:
http://en.wikipedia.org/wiki/Constituti ... s_starship)
Constitution-class was the only major ship class seen in the original series. Other Starfleet capital ship types include the Miranda class of the live-action films, and the older design of Bonaventure, seen in the animated episode "The Time Trap".
Though now understood as such, the class was never named Constitution in the original series; Enterprise's bridge dedication plaque declares her a 'Starship' class vessel, and it was also referred to as a "Starship" in the episode " The Enterprise Incident". The designation "Constitution-Class" debuted in 1975 in Franz Joseph Schnaubelt's Star Fleet Technical Manual. Its subsequent usage in show creator Gene Roddenberry's novelization of the first film cemented its usage in Trek fandom thereafter. (His novel also set K't'inga as the Klingon class name for the film's refinement of the venerated D7 battlecruiser.) The Star Trek: The Next Generation episode "The Naked Now" tags the original Enterprise as a Constitution class ship, fixing it in canon; a diagram seen in Star Trek VI: The Undiscovered Country puts Enterprise A in the Constitution-class as well.
The Next Generation episode "Relics" puts a Constitution-class vessel in the Starfleet museum.
The novelizations of the second, third, and fourth Star Trek films, written by Vonda N. McIntyre, identified the Enterprise as a "Constellation-class" heavy cruiser. This was overridden by the Next Generation episode "The Battle", in which the USS Stargazer was listed as Constellation-class, rather than Constitution.
It definitely piqued my interest. Remember, though, in NuBSG (about which the book was written), the Colonials derive their culture from Greco-Roman mythology, as opposed to TOS's more Egyptian-themed mythology. Jupiter definitely falls within that established pantheon.