Book as usual and, when you're asked Who's it for?, pick someone from your household or choose Someone else and add their name. The booking stays in your account, so you get the emails and you pay.
Start a booking
Pick the service and the time as you normally would.
Choose who it's for
The step asks Who's it for? and lists you, then everyone in your household. Pick one.
Or add someone new
Choose Someone else and type Their name. They're added to your household for next time.
Check and book
The Check step shows who it's for under For. Choose Change if it's wrong.
The question changes with what you book. A dog groomer asks Which dog?, a valeter asks Which car?, and a children's class asks Which child? or Who's coming?. A visit to your home asks Where should we come? and lists your places.
Household in your account holds the people, pets, places and vehicles you book for. Choose Add, pick what it is (Person, Pet, Place or Vehicle) and give it a name and a few details.
A business sees an entry only when you book for it, and only the details you added. To stop a business using an entry, open it and choose Stop sharing next to that business.
Sometimes a business adds someone for you, like a dog they groomed. It shows as Suggested by the business. Open it and choose Yes, keep or No, remove.
Some classes let you book places for friends who don't have an account. Under Guests, add Guest places. You book and pay for them.