Traditionally, the four pastas of Rome are carbonara, cacio e pepe, alla gricia, and amatriciana.
You get alla gricia from a cacio e pepe by adding guanciale bacon(pork jowl), and adding egg on top of that gives you carbonara.
My question is: if you were to make pasta involving cheese, pepper, eggs and pasta water, but no guanciale, what would that pasta be called? Is there a "proper" name for it? Or would you just say "carbonara without baconguanciale/cacio e pepe with eggs"?