We don't name them immediately, once their personalities developed, we gave them names.
Galadriel is a stately white Ameraucana
Goldilox is her blonde sister
Coco and Bluebonnet are the Reds.
Chewie survived the dog attack
Terry looked like a pteradactyl as a tweenie
Duckie looked like a duck as a tweenie
Sweetie is the sweetest one
The meaties have names like
A La King
Kiev
Cordon Bleu
Leftovers
Dinner
Enchalada
but as a group are referred to as the "McNuggets"
As for knowing which hen laid which egg, there are 'trap nests' you can make but you have to let the hen back out once she has laid. Then you can mark the egg with the hen's ID.