I usually name my chickens based, at least in part, on their country of origin or a favorite character.
My Speckled Sussex, a British breed, got a British name, Bronwyn, that's also the name of a character from a movie I love.
Eleanor, a Maran, is named for the French queen, Eleanor of Aquitaine, a very brave ruler.
The Buckeyes, all-American girls, are named for three TV characters: Althea, Beatrix and Cordelia.
Once in a while, I break down and name them for physical features. Honey is a golden beautiful Buff Orpington, and one of my Cochin Bantams is named Gabby because she talks all the time. My roo, an Iowa Blue, is named Sir Henry the Loud because he is.
Good luck with choosing names. I've never had to deal with a mongoose, but I have had trouble with minks. Burying hardware cloth and wrapping the runs in it, not chicken wire, may help.
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