Well, I put 4 openings starting with Aa and Ab.
Game: List of openings by proper names: A

albin (you forgot people can check on internet)
Please check and we will get a complete list!

I'm gonna put a few sources here.
link- https://www.angelfire.com/co/frostschess/chessopenings.html
I will have more
not very complete but here are the openings here-
1. Nf3 d5 2. e4 dxe4 3. Ng5
Adorjan Gambit
1. d4 Nf6 2. c4 g6 3. d5 b5
Agincourt Defense
1. d4 Nf6 2. c4 g6 3. d5 b5
Alapin's Opening
1. e4 e5 2. Ne2
Alekhine's Defense
1. e4 Nf6
Alekhine's Defense
(Brooklyn Defense)
1. e4 Nf6 2. e5 Ng8
Alekhine's Defense
(Exchange Variation)
1. e4 Nf6 2. e5 Nd5 3. d4 d6 4. c4 Nb6 5. exd6
Alekhine's Defense
(Four pawns attack)
1. e4 Nf6 2. e5 Nd5 3. d4 d6 4. c4 Nb6 5. f4
Alekhine's Defense
(Modern Variation)
1. e4 Nf6 2. e5 Nd5 3. d4 d6 4. Nf3
Alekhine's Defense
(Retreat Variation)
see Brooklyb Defense
Alekhine's Defense
(Two pawns attack)
1. e4 Nf6 2. e5 Nd5 3. c4 Nb6 4. c5 Nd5
Aleppo Gambit
See Queen's Gambit
Amar Gambit
1. Nh3 d5 2. g3 e5 3. f4 Bxh3 4. Bxh3 exf4 5. O-O
Amazon
1. d4 d5 2. Qd3
Anti-Grünfeld System
1. d4 Nf6 2. c4 g6 3. f3

http://www.eudesign.com/chessops/ch-index.htm look through this one
Let's play a game, suggest your opening (proper name) starting by letter A. I will rearrange it in the alphabetical order.
Remark: each name could appear only once (the most popular variation with this name). 
Aachen gambit:
Abbazia defense:
Abonyi variation:
Abrahams variation:
Adams attack:
Adler variation:
Adorjan defense:
Agincourt defense:
Alapin variation:
Albin countergambit:
Alekhine defense:
Amar opening:
(to be continued
)