How many opening moves are needed before we can identify that such moves fall into a particular well-known opening such as Ruy Lopez, London, kings gambit, an so on?
It depends on the opening. Some are more strictly defined than others; e.g. a game is really only a "Ruy Lopez" if it reached the position after 1.e4 e5 2.Nf3 Nc6 3.Bb5, but lots of different lines where white plays an early d2-d4 and black's ...c7-c5 is answered by d4-d5 are called "Benoni".
Some variations have a well-known name on move 12-ish (like the Soltis variation in the Dragon), whereas a major line used in world championship matches like 1.Nf3 d5 2.g3 g6 doesn't even have a real name at all.
There's really no logic to it, it's a bunch a historical accidents and traditions.
But these are only the names of openings. They are useful when talking to somebody about your game, or when you need a title for your new book or you are looking for a book, and for nothing else.
They are completely unrelated to how much a given player knows about some opening. Especially opening books often start from some named position.