Rome is a place and, despite it's "brutal" nature, the Empire has endured in archaeology and literature. I don't see it as completely inappropriate (except that there are only seven hills...what happens when they build an 8th ship of that class?).
That said, this is one way in which Star Trek mirrors modern military practices. All classes of U.S. Navy vessels (and ships from other navies, too, I'm sure) have a naming convention.
Nimitz-class carriers are named for great supporters of the Navy (Nimitz the fleet admiral, Vinson and Stennis were champions of the Navy in Congress, Lincoln and Washington our greatest presidents, Roosevelt a former Secretary of the Navy and later president, G.H.W. Bush a naval aviator in WWII and later president, Reagan and the 600 ship Navy, and so on).
Los Angeles-class fast attack submarines are named after American cities, and the Ohio-class ballistic missile submarines and Virginia-class fast attack submarines are named after U.S. states.
And so on. Even Starfleet's Constitution-class cruiser has a naming convention. All of the ships are named for famous Earth vessels.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz