I'll play the male character first, and I'll name him Bob. That's the only name I've ever used for a male character in Pokemon games (and, in fact, in almost all games). It's just automatic - whenever a game asks for a character name and it's not otherwise important to me, I name him Bob.
If the female player character appears in the game as an NPC if she's not played (like in RSE or DPPt), then the odds are that I won't ever play her, since she'll be a part of the game anyway. If she doesn't appear in the game at all unless she's played (like in FR/LG or B/W) then I'll probably play her, and she'll be named Ann, just like the others.