He seems to have a great love for animals, such as kitty cats and bunny rabbits. In the episode Shrinkin' in the Ray, he 'accidentally' used Two-Brains' growth ray on his pet bunny, Flopsy, and became sad and worried when Flopsy was too big to bring along on their next evil mission.
In A Game of Cat and Mouse, it was revealed that he actually has a full head of well-styled hair hidden under his cap.
The only time that Dr. Two-Brains called his unnamed henchman by any name was "Meatloaf", after the henchman was saying something about his mom's meatloaf in Kids Action News. The reference appears to be sarcastic and was never used again, so it should not be implied to be an actual nickname.
In Dr. No-Voice, Nick Michols, Two-Brains' voice fill-in, referred to him as "Henchman number 1."