This name generator will generate 10 names, which will generally fit most types of rodents, like hamsters, squirrels and other critters. pocket gopher family (Geomyidae). Names for gerbils, guinea pigs, hamsters, mice, rats, etc. [ Suggest Names for this page ] [ Go to Pet Names A-Z Page ] They feed on crops and contaminate produce with their feces, saliva and urine. These rodents burrow for shelter, thereby destroying planted areas and root systems. There's a whole range of critters out there who aren't often named, and also don't make for very great pets. Small rodents such as gophers, moles, rats and mice may also prove to be pests in agricultural communities as well as in residences. kangaroo mice and rats (family Heteromyidae). Names that mean beaver, hare, mink (not really a rodent), mole, mouse, porcupine, rabbit, squirrel, weasel (not really a rodent), etc. Pet rodent name generator . suborder Castorimorpha beaver family (Castoridae).