Please let me know if I forgot something.
Collection of King's Pawn 2Ee-Openings

Italian Game, Two Knights Defense, Knight Attack, Normal Variation (+0.1) 46/23/31
Ponziani Opening (+0.1) 33/37/31
Ponziani Opening, Reti Defense (+0.3) 50/13/27
Ponziani Opening, Ponziani Countergambit (+0.6) 49/19/32
Vienna Game, Vienna Gambit (0.0) 30/39/31
King's Gambit (-0.7) 30/34/36
Ruy Lopez, Jaenisch Gambit (+0.6) 40/40/20
Ruy Lopez, Jaenisch Gambit, Dyckhoff Variation (+0.4) 41/42/17
Ruy Lopez, Jaenisch Gambit, Schoemann Attack (0.0) 34/30/36
Italian Game, Rosseau Gambit (+1.4) 58/33/8
The common point of all these openings is that they start from King's Pawn Game 1.e4 e5 and don't change this 2Ee-pawn structure. They also have traditional names. I indicate their evaluations from ChessOK database.
Historical games (first occurences):
King's Knight Game: 1.e4 e5 2. Nf3 | Damiano - NN (1497, 1512), Ruy Lopez - Da Cutri (1560).
Petrov Defense: 1. e4 e5 2. Nf3 Nf6 | Damiano - NN (1497).
Giuoco Piano: 1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 | Scovara - Boi (1575).