"The following names have been established for starships: Enterprise, Exeter, Lexington, Yorktown, Potemkin, Republic, Hood, Constitution, Kongo, Constellation, Farragut, Valiant, and Intrepid. The latter four are listed as destroyed in various episodes." - The Making of Star Trek, p.165.
Notes on this claim:
1.) I have no memory of the name Kongo appearing in aired Trek.
2.) "Obsession" only establishes that the Cloud Creature killed half the crew, not that the Farragut itself was destroyed.
3.) The Valiant listed is presumably the one that was lost at Eminiar VIi fifty years earlier (or ca. 2217), or some 28 years before the Enterprise entered service in 2245.
4.) A reference elsewhere in TMoST claims that starships of the class to which the Enterprise belongs have been in existence for forty years (by TOS), so since ca. 2227, contradicting the assumption that the Valiant lost at Eminiar VII was a Connie.
5.) If that Valiant wasn't actually a Connie, it's possible that the Republic (NCC-1371) and the Farragut weren't also.
6.) Alternately, it's possible that there was a class of starships that looked much like Constitution-class starships constructed between ca. 2227-2245 with NCC numbers lower than 1700 - like the Sombra-class starships, and the Constellation (NCC-1017) and possibly the Republic (NCC-1371) and all those presumed Connies with registry numbers in the NCC-1600 range (except obviously the Farragut as of SNW) were actually constructed as Sombra-class vessels.