How do Japanese native speakers write their name in Romaji/English?

Does the surname still come first? Or do they write their name as English speakers would; first name, then last name? I am corresponding with a Japanese hotel receptionist in English and I this person's first and last name could be either/or; a first or a last name, so I'm not sure how to address him/her? Thank you, Maude

Order: Family name, Given name