Not Romanian, but you usually need to make an appointment at a barber (especially now that they can't/don't want to have too many people in their shop at once, due to COVID regulations). If you make the appointment online, then you can usually create an account to view/rebook/cancel it later, if necessary.
I book my hair appointment online. they ask for name, email and mobile phone number. They need the name to know who to expect for the appointment. They ask for email and/or phone to send you a reminder (which is nice, IMO).
Very reasonable and totally with the GDPR rules as well, as long as they purge the data after a certain time.