I never tipped my groomer all these years either. But beginning last year, I started giving her $5 more because my senior pup is becoming a bit more difficult to clip because of weakness in her legs, blind, deaf,ect. Jenny is very good with her. Before I always thought I paid her enough, so never tipped.

I use PetSmart grooming and always request the same person each time. She's great with my dog, gives him extra attention and understands all his little quirks.
When paying for the grooming at PetSmart you check out thru the cashier in the front of the store, so if my dog's groomer isn't there when I pick him up (which is common)tipping her can be difficult. Instead, I give her a big tip each Christmas. When I drop him off for his Dec. grooming, I give her either cash or a gift card to a local store.

Re: the store asking for the check made out to them, they may be combining all the tips and then splitting the total between the groomers.
If you want to tip a specific groomer then you should tip her directly, not with a check made out to the store.