GCP(2Ec, 2E1e) = 2E King's Pawn Opening,
LCH(2Ec, 2E1e) = 2Ec1e Sicilian Defense: French Variation.
You didn't explain your 3-digit/4-digit/5-digit notation. I figured it out, but most readers aren't going to go to the trouble to do that.
One major problem with this whole idea is that human brains don't remember things well when they're written with letters and numbers. For example, one database shows one opening called "Queen's Gambit Declined, 4.Bg5 Be7." Get real! Can you imagine trying to remember, pronounce, or interpret the spoken name of that opening? I guess one would say: "Queen's Gambit Declined Four Bee GeeFive Bee EeSeven." It gives me a headache to even look at that.
I came up with what I believe is a better scheme where I use 3-letter mnemonics for each move. For example:
...a6 = -naj- <= Najdorf Sicilian
...e6 = -fre- <= French Defense
...h6 = -lev- <= Levitsky Attack
Nb3 = -bol- <= Boleslavsky Sicilian
Nc3 = -dun- <= Dunst Opening
Nd2 = -tar- <= Tarrasch French
Therefore if a variation involved the moves Nc3 ...a6 together, I would call it the Dunnaj Variation. That's very pronounceable, and those mnemonics are usually concatenatable. That method has the drawback of a huge number of theoretical piece-square combinations, but in practice only a manageably small number of those possibilities is commonly used. I've been using that system without much trouble for the past year.
Definition 1. Suppose that we have 2 different legal pawn structures P1 and P2. P1 will be called a predecessor of P2 and P2 a successor of P1 if there exist legal positions A and B with pawn structures P1 and P2 respectively such that B can be obtained from A by a sequence of legal moves.
The notion of pawn height is introduced here:
https://www.chess.com/forum/view/chess-openings/pawn-structure-classification-codes
Definition 2. Let P1 and P2 be 2 pawn structures. The greatest common predecessor GCP(P1,P2) is the predecessor of both P1 and P2 having the highest pawn height. The least common successor LCS(P1,P2) is the heritor of both P1 and P2 having the lowest pawn height.
Example 1. Let P1=2Ec Sicilian Defense and P2=2E1e French Defense then
GCP(2Ec, 2E1e) = 2E King's Pawn Opening,
LCS(2Ec, 2E1e) = 2Ec1e Sicilian Defense: French Variation.
It's a good way to give names to unnamed opennings.
Example 2. Let P1=2DEe Scotch game and P2=2Ee1d Philidor Defense then
LCS(2DEe, 2Ee1d) = 2DEe1d
can be called Scotch Game: Philidor Variation.