2 It is not mandatory that a club designate a hitter for the pitcher, but failure to
do so prior to the game precludes the use of a Designated Hitter for that club
for that game.
10 Once the game pitcher bats for the Designated Hitter, such move shall terminate the Designated Hitter role for that club for the remainder of the game.
The game pitcher may pinch-hit only for the Designated Hitter.
12 Once a Designated Hitter assumes a position on defense, such move shall terminate the Designated Hitter role for that club for the remainder of the game
These rules combine to indicate quite clearly that the Pitcher cannot be named the designated hitter for himself. Specifically 12 would be the clearest case, the DH cannot appear on defense, which is the primary role of the pitcher.
What a team could do if they had a pitcher with sufficient value as a DH though is the have him DH and then allow him to pitch, perhaps in a closer type role. Though rule 15 indicate that he would not be allowed to warm up in the bullpen:
15 The Designated Hitter may not sit in the bullpen unless serving as a catcher in