to be more respectful (If you are asking to a stranger or a senior but not to someone young) 성함을 여쭤봐도 되겠습니까? (실례지만) 성함을 가르쳐 주시겠습니까?

한국 이름은 뭐예요? - What is your Korean name? (If you know they have one) If you want to ask if they have one - 한국 이름은 있습니까?