What criteria should I apply to settling on something suitable?
The job of choosing a name for a working dog is too important to be treated lightly: something short and sharp is what’s needed, but you (as its handler) will also have to like the name.
By all means listen to what your kids come up with but it’s you who needs to have the final say.
It might help to look at the pup’s pedigree because sometimes it might have the most appropriate name hidden away as part of the kennel name.
I remember going to look at a litter of cocker pups and saying, as one came running toward me: “With a black patch like that over his eye he’s got to be a bandit,” and that’s still its name 12 years later.
I know of one shooter who names his dog after the one it is replacing but while that might not be for you, just remember whatever you call the pup, you’re going to be shouting his name in the field.
In this respect I think “Sam…heel” is far better for the dog and your credibility than “Peregrine…come here!”