Very interesting! Meeting and aardvark or anteater is a current top priority on my non-owl list of animals I must encounter. I've seen them at zoos, but we have always been on opposite sides of the display, which I'd like to remedy at some point.
I couldn't find anything saying that anteater was his actual pet. The baby one he took on Dick Cavett was a loaner from the Bronx Zoo, and from all I could find, the one from the Paris photo was also most likely borrowed from a zoo. (Ahhh, the things one could do with animals before we collectively decided they may have conciousnesses of their own...)
It sees he did actually have a "pet" ocelot, given to him by a Columbian head of state. It's name was Babou, and is apparently the inspiration for Cheryl's ocelot Babou in the cartoon series Archer.
The Dick Cavett interview is a real trip. The poor baby anteater gets tossed on the floor, a table, and finally launched on the guest actress by Dali and even she scolds him saying he scared the poor thing.