In the world of comics, superheroes - like movies - have sequels. This wasn't always the case, and, confusingly, still isn't; Superman is still Clark Kent and Batman is still Bruce Wayne (Let's just ignore that whole "Battle For The Cowl" thing for now, huh?) despite the fact that they've fought for justice alongside multiple Green Lanterns, Flashes and even Green Arrows. Leaving aside the tricky question of just how aging works for superheroes, Watchmen's "legacy characters" - to use a comic term for superheroes who pass their costumes and names onto others - are each an important part of the world in which the story takes place; Silk Spectre II is the daughter of the original Silk Spectre (Much in the same way that one of Moore's inspiration for the character, DC's Black Canary, was revealed to actually be her own daughter in a ridiculous 1980s storyline that preceded Watchmen's release), while the second Nite Owl was inspired to take up the cowl by the original, Hollis Mason, whose presence haunts Watchmen in more ways that one.
This does not mean, however, that you should expect to see superheroes with names like Nite Owl: The Revenge or Silk Spectre: A New Beginning. That would be dumb.