If only. The USS Enterprise (CV-6) was actually the seventh vessel to bear the name. By the time Star Trek was airing on television, there was already another supercarrier named USS Enterprise (CVN-65), the only ship of her class. She was in service from 1961 until 2012, and decommissioned only last month.
The next Enterprise will be a Gerald R. Ford-class aircraft carrier, CVN-80.