OK, so it seems only one diagonal has an official name, so let's move on to step 2, where we invent names for the remaining, nameless diagonals. Who wants to show off their knowledge and/or creativity?
I came up with the following ideas, mostly based on openings that use those diagonals, but I'm getting stuck since I don't know enough openings and which diagonals they use to fill in the rest. Also, I'm not particularly happy with some of my names.
ending squares, all squares, # of squares, English name:
a8-a8 a8 1 (a single square)
a6-c8 a6-b7-c8 3
a4-e8 a4-b5-c6-d7-e8 5 "Spanish Diagonal"
a2-g8 a2-b3-c4-d5-e6-f7-g8 7 Italian Diagonal
b1-h7 b1-c2-d3-e4-f5-g6-h7 7
d1-h5 d1-e2-f3-g4-h5 5
f1-h3 f1-g2-h3 3
h1-h1 h1 1 (a single square)
a7-b8 a7-b8 2
a5-d8 a5-b6-c7-d8 4 "Caro-Kann Diagonal"
a3-f8 a3-b4-c5-d6-e7-f8 6
a1-h8 a1-b2-c3-d4-e5-f6-g7-h8 8 (a long diagonal) "Larsen Diagonal"
c1-h6 c1-d2-e3-f4-g5-h6 6
e1-h4 e1-f2-g3-h4 4 "Fool's Mate Diagonal"
g1-h2 g1-h2 2
g8-h7 g8-h7 2
e8-h5 e8-f7-g6-h5 4 "Scholar's Mate Diagonal"
c8-h3 c8-d7-e6-f5-g4-h3 6
a8-h1 a8-b7-c6-d5-e4-f3-g2-h1 8 (a long diagonal) "Hungarian Diagonal"
a6-f1 a6-b5-c4-d3-e2-f1 6
a4-d1 a4-b3-c2-d1 4 "Rubinstein Diagonal"
a2-b1 a2-b1 2
a1-a1 a1 1 (a single square)
a3-c1 a3-b2-c1 3
a5-e1 a5-b4-c3-d2-e1 5 "Bogo-Indian Diagonal"
a7-g1 a7-b6-c5-d4-e3-f2-g1 7
b8-h2 b8-c7-d6-e5-f4-g3-h2 7
d8-h4 d8-e7-f6-g5-h4 5
f8-h6 f8-g7-h6 3
h8-h8 h8 1 (a single square)
DERIVATION OF ORIGINAL NAMES (alphabetical)
"Bogo-Indian Diagonal": diagonal where Black checks in the Bogo-Indian: 1. d4 Nf6 2. c4 e6 3. Nf3 Bb4+
"Caro-Kann Diagonal": diagonal along which Black's queen often attacks in the Caro-Kann
"Fool's Mate Diagonal": diagonal on which White is mated in Fool's Mate: 1. f3 e5 2. g4 Qh4#
"Hungarian Diagonal": diagonal covered in the Hungarian Opening (Benko's Opening): 1. g3
Italian Diagonal: diagonal covered in the Italian Game: 1. e4 e5 2. Nf3 Nc6 3. Bc4
"Larsen Diagonal": diagonal covered in the Nimzovich-Larsen Attack: 1. b3
"Rubinstein Diagonal": diagonal along which White's queen moves in the Rubinstein Caro-Kann
"Scholar's Mate Diagonal": diagonal of mate in Scholar's Mate: 1. e4 e5 2. Qh5 Nc6 3. Bc4 Nf6 4. Qxf7#
"Spanish Diagonal": diagonal of the pin in Ruy Lopez (Spanish Opening): 1. e4 e5 2. Nf3 Nc6 3. Bb5
So far I've seen a name for only one of the diagonals on the chessboard: the "Italian diagonal," which runs through f7 from a2-g8, probably named after the Italian Game opening, where White's king bishop uses that diagonal.
http://exeterchessclub.org.uk/content/italian-game-beginners
http://franosch.org/chess/italian.pdf
Does anybody here know of any other diagonals with names? It seems to me another important diagonal for White's tactics would be the diagonal that runs to h7, which is a common spot for a bishop sacrifice from White.