You can register several collars on a single machine. You can also name the cat that has a collar, but this is mainly for subscription purposes (monitoring your cat's diet).

Hi. But I actually have 2 collars for 1 distributor and it works perfectly.

No, pairing is only possible for 1 cat per machine. Each cat has a collar with a chip, which is paired to the vending machine. If you have 2 cats, you need 2 vending machines