What Yangmin 씨 said is correct. What Tom mention is actually too formal. Yangmin's answer is most commonly used in my opinion :) 이름이 뭐예요? = ireumi mwoyeoyo is how you romanized it, assuming you dont read hangul yet... [ee-reum-ee mo-yo-yo] is how you pronounce it. ^_^

We can say in many different way to say "What's your name?" but the most formal expression is "이름이 뭐예요?" That's not kind of humble expression but more casual :) '이름' which means "name" '이' is like postpositional word. I think that's not easily understandable for foreigners. Korean has more several postpositional word like '이'. They are '는', '가', '를' etc.. It's little bit hard to explaining about it but simply it's almost same like 'is' or 'are' of English. '뭐예요?' = 'What?'

What is your name? 당신의 이름은 무엇입니까? (Dang Shin Eui E Reum Eun Moo Et Im Ni Kka?) Have a good day!

이름이 뭐예요?: What is your name: 이름: name 뭐: what 제 이름은 Jessica 이예요.: My name is Jessica. 제: my Hope it helps! :)