This are the names the Expanded Universe books came up with. (copied from Memory Beta Wiki)
ship name registry ship commissioning disposition
Enterprise NX-01 2151,[1] refit 2156[2] decommissioned (2161)[3]
Columbia NX-02 2154,[4] refit 2410[5] destroyed (2156)[6]
active (2410)[5]
Challenger NX-03 2155[7] destroyed (2156)[7]
Excalibur NX-03 2155/56[6] destroyed (2156)[6]
Discovery NX-04 2155[7] destroyed (2155)[7]
Constellation NX-04 2156[6] active (2160)[6]
Atlantis NX-05 2156[7] destroyed (2156)[7]active (2160)[6]
Slayton NX-05 by 2159[8] active (2261)[8]
USS Endeavour NX-06, NCC-06 2156,[7] refit 2161[9] active (2165)[10]
Defiant NX-06 or NX-07 2156[6] destroyed (2160)[6]
Lexington NX-06 or NX-07 2156[6] active (2160)[6]
Intrepid NX-07 circa 2160[11] destroyed (2384)[11]
Avenger NX-09 by 2159[12] active (2159)[12]
Currie NX-16 by 2159[12] active (2159)[12]
Utopia NCC-2151-01 2409[13] active (2410)[13]