Neighbours, schools and government systems will assume a missing child if they move out of their homes to Hogwarts. How do they keep their old identities in sync with going to a place unrecognised by muggles?
Going to Hogwarts is no different from going to any other boarding school. They disappear during the school term and reappear over the holidays; it would be easy for parents to explain that they are at a boarding school. For example, the Dursleys made Harry tell Aunt Marge that he attended St Brutus's Secure Centre for Incurably Criminal Boys.