I looked up the ECO code (which is C50) for the moves 1.e4 e5 2.Nf3 Nc6 3.Bc4 and found the following names listed for the various moves:
C50 Italian Game; C50 1.e4 e5 2.Nf3 Nc6 3.Bc4
C50 Giuoco Piano; Italian Opening 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5
C50 Jerome Gambit; Kentucky Opening 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Bxf7+
C50 Giuoco Pianissimo 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d3
C50 Lucchini Gambit; Italian 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d3 f5
C50 Italian Four Knights Variation 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d3 Nf6 5.Nc3
C50 Canal Variation, Italian 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d3 Nf6 5.Nc3 d6 6.Bg5
C50 Rosentreter Gambit, Italian 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.d4
C50 Italian Variation, Four Knights Game 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.Nc3 Nf6
C50 Deutz Gambit, Italian 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.O-O Nf6 5.d4
C50 Hungarian Defense 1.e4 e5 2.Nf3 Nc6 3.Bc4 Be7
C50 Tartakower Variation, Hungarian 1.e4 e5 2.Nf3 Nc6 3.Bc4 Be7 4.d4 exd4 5.c3 Nf6 6.e4 Ne4
C50 Half Giuoco Piano; Semi-Italian Opening 1.e4 e5 2.Nf3 Nc6 3.Bc4 d6
C50 Rousseau Gambit 1.e4 e5 2.Nf3 Nc6 3.Bc4 f5
C50 Shilling (Kostic) Gambit, Italian 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nd4