So here are all the names we have given them so far (you can spot our literary interests)

He: Rob Anybody
Fear Nothing
Mishka (Russian)
Chieftain
Gimly (current winner)

She: Mittens
Pictsie
Cheburashka (Russian)
DR
Galadriel (current winner)

Both:
Wee Free Kittens
Nac Mac Feegles
Little Bottomless Pits
Wojska Lulasia (Polish)