They still could use Conner without setting the fifth season before the final episode. All they have to do, is to write it into the stroy that Trip had a twin brother.
A starship name Enterprise can be use after 2161. Remember that in first season of star trek, maybe the second season as well, the NCC-1701 was a United Earth ship, not a federation ship. It didn't come a federation ship until second or third season.