This doesn't take alternate forms into account
A - 594
B - 133
C - 193
D - 187
E - 529
F - 83
G - 196
H - 164
I - 443
J - 13
K - 130
L - 390
M - 207
N - 368
O - 266
P - 187
Q - 12
R - 463
S - 308
T - 324
U - 253
V - 56
W - 90
X - 31
Y - 107
Z - 45
I've also included a few non-letter symbols/characters:
- [Dash] - 5
. [Period] - 2
' [Apostrophe] - 1
♀ [Female symbol] - 1
♂ [Male symbol] - 1
: [Colon] - 1
2 [Number two] - 1
é [Accented E] - 2
Source: Copying and pasting this list into a Google doc, using the find and replace function to remove all of the types, (yes, I did make sure that, for Pokemon like Darkrai, I readded the type that was in their name) and then using the same find and replace function to see how many of each letter was in each Pokemon's name.