이름이 뭐예요 is polite and common. 어떻게 되세요 is more respectful and formal, great for elders or business.
No, 이름 뭐야 is casual. Use only with close friends same age or younger. To be safe, use 이름이 뭐예요?
Say 저는 ~라고 해요 (jeoneun ~rago haeyo) or ~입니다 (~imnida) for polite. Casual: ~야 (~ya).
이름이 뭐예요? means "What's your name?" in polite daily Korean. 이름 (ireum) = name, 뭐예요 (mwoyeyo) = what is it? Most common way to ask name at first meeting. For elders use 어떻게 되세요?
1. First meeting friends: 이름이 뭐예요?
2. Elders / business: 이름이 어떻게 되세요?
3. Same age casual: 이름 뭐야?
What's your name? I'm Minjun.
May I know your name? I'm Suyeon Kim. (Very polite)
What's your name? I'm Sua. (Casual)
Nice to meet you. What's your name?
• 성함이 어떻게 되세요? (seonghami eotteoke doeseyo?) - Very formal for name (honorific)
• 이름이 뭐야? (ireum mwoya?) - Casual what's your name
• 어떻게 불러드릴까요? (eotteoke bulleurilkkayo?) - What should I call you?