Is there an official name for the pasta in between carbonara and cacio e pepe?

Question

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 (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 guanciale/cacio e pepe with eggs"?

Answer 1

From a quick google search, it seems to be named "cacio e uova", uova in Italian means eggs.

If you can read italian this giallo zafferano recipe might help https://ricette.giallozafferano.it/Pasta-cacio-e-ova.html

Here in Italy some people including my family put cream instead of eggs so if you were to give it a name it would probably be called "cacio e crema" but personally I would just stick to the conventional recipes.