I think "Starfleet" is a pretty darn generic name for a fleet of starships. And according to the OED
, it's been used in other works of fiction besides Star Trek
, and while ST popularized the term, there's at least one documented use of "star fleet" preceding ST, from a 1939 story by Lester Del Rey.
Besides, at the time the Commonwealth comes into being, the Terran Empire's been extinct for over 85 years. I think more people would remember the tyranny of the Klingon-Cardassian Alliance by that point.