There is no shared household account, and that is deliberate. A Beauty Passport holds formulas, sensitivities and treatment history, and merging two people's into one produces a record that is wrong for both — a colour formula for one head of hair is actively misleading applied to another.
So: an account each, for anybody old enough to have one. Everybody keeps their own history, their own reminders and their own passport, and a professional sees the right record for the person in the chair.
For a child or anybody you book on behalf of, book under their name from your own account and say in the notes who is attending and who is paying. That keeps the studio informed even though the history sits with you.
Paying is separate from the account. You can pay for somebody else's appointment at the studio regardless of whose account made the booking, and a gift card does the same thing without any account juggling at all.