USS Enterprise (NCC-1701-A)
USS Enterprise (NCC-1701-B)
USS Enterprise (NCC-1701-C)
USS Enterprise (NCC-1701-D)
USS Enterprise (NCC-1701-E)
USS Enterprise (NCC-1701-F)
USS Enterprise (NCC-1701-G)
To anyone who has not seen Lower Decks, and either doesn't want to or can't:
Rumdar is a Pakled (the "It Makes Us Go", "capture Geordie and force him to make them strong" dumb guys)
When the captain of the USS Cerritos meets this Pakled (and others) they all call her Janeway (because she's a woman and in starfleet, therefore either she must be captain Janeway or all female captains are named Janeway)
They also refer to the Cerritos as "Enterprise", as well as the USS Titan, which they call "Another Enterprise", so either they think all ships are coincidentally named Enterprise , or all starfleet ships are called Enterprise.
I don't know about in Trek lore, but I think in the real world, when a ship is designed or used to travel from one star system to another, it's classified as a starship