Polite form of 名前 used when referring to someone else's name, especially in formal or customer-service contexts.
May I ask your name?
We will ask for your name when you place your order.
Excuse me, but may I ask your name?
Please give your name at the reception desk.
Please write your name in this space.
名前 is the plain, neutral word for 'name', while お名前 adds the honorific お- prefix to show respect when asking or referring to someone else's name.
Honorific prefix お + 名前 (name).