At what point during an opening variation does the naming of the variations stop?

I recently ran into a very weird opening player. This is the black opening he played-

Yeah, it's kind of strange, but 3 moves deep isn't too strange to have a name.

Yeah but 3 moves in, in a very unusual line one would think openings wouldn't have specific names.

But it isn't a very unusual line.

1. e4 a6 2. Nf3 c5 gives you EXACTLY the same position as 1. e4 c5 (Sicilian Defense) 2. Nf3 a6 (O'Kelly Variation).

That's called 'a transposition', and in this case the odd and unusual 1. ... a6 transposed to a very well known line in the Sicilian, which itself is probably the most common reply to 1. e4.

No one bothers to learn all those 100s of names, that I can promise you. It's more of a silly feature of databases.

Experienced/skilled players just go by pawn structure. First of all there aren't many different pawn structures, so that's nice! But also since pawns can't move backwards they're an enduring feature of any position, and they set the tone and strategic themes of the game, particularly when a center pawn is moved.

This is how an experienced player sees the same sequence:

And I don't even play the sicilian, so there are probably various subtle move order tricks in some of those moves that players can be using to transpose into (or avoid transpositions into) various lines.

But the important point is that chess isn't some endless sea of variations. The pawns set the tone, and there are only roughly one dozen or so main structures in all of chess.

This is why opening study isn't so important. As long as you understand the middlegame (and with a little trial and error avoiding super sharp lines) you should be able to get a playable position vs anything.