One of the things I plan to make in the near future is Pasta Carbonara. I would say essentially traditional - I even found some guanciale (although pancetta is also accepted - even bacon sometimes, especially since guanciale is hard to find in some parts of the world). It will be a fun cooking experiment since getting the eggs right to make the carbonara part will require mastering a technique I am atm uncertain about. It won't have tomatoes (or peas). It may have the wrong type of pasta in it as I don't like spaghetti pasta, for reasons not fully pertinent to this discussion. Right now, as I have ALL the ingredients needed (my choice of long pasta, pecorino Romano, eggs, guanciale, ground pepper) - just waiting for an appropriate headset to create this. Won't be this week, or the COVID second shot next week recovery, but hopefully after.
I believe that being able to communicate with others is an appropriate thing to do, and as one who does a food blog, I'd rather say something like: Greek-Inspired Gluten-Free Meatballs, than to mislead someone with an inaccurate title, someone who is expecting to find a traditional version of something when they waste their time opening up the link to my blog. I would never call a banana gnocchi a carbonara, at least for that very reason. At least not in public. I would also not make a French onion soup with beef broth and call it a vegetarian French onion soup. (A few years back I went with some vegetarians out to dinner, and they ordered French onion soup... made with beef stock, as it turned out...)
I will note some cultures are more picky than others - it seems that many Italians (and, French) can be more prickly about their nomenclature and exactitude of recipes than say, the Chinese or Korean people. In India, so many recipes have their own variants, from family to family. So I can make an Indian curry, and not have to call it "Indian-inspired curry" unless I'm using ingredients that have never touched that sub-continent's soil, like, say, a bolus of Jerusalem artichokes.
So... regards carbonara. There's American carbonara, and there's Italian carbonara. In this case, different levels of flexibility in how one discusses or prepares each.
.On another note, you wouldn't believe the abominations people come up with in restaurants and cook books in the name of Italian Cooking...It would make you cringe..even I have a problem with many of the recipes