Learn Arabic (Modern Standard): مرحبا، ما اسمك؟

In Arabic, there is no direct equivalent for the present tense of the verb "to be" (am, is, are). You simply put the parts of the sentence side by side. So, ما اسمك literally translates to "What your name?".

I've learned that ماذا means "what". Why does this sentence use ما instead?

Both ما and ماذا mean "what", but they are used in different situations. You use ما before nouns, like اسم (name) in this sentence. You use ماذا before verbs, for example when asking "What are you doing?".

How do I know if I'm asking a man or a woman, since اسمك looks exactly the same for both?

Arabic writing usually leaves out the short vowel marks (tashkeel). The spelling اسمك adds the suffix ـك ("your") to the word اسم ("name"). If you are talking to a man, you pronounce it ismuka. If you are talking to a woman, you pronounce it ismuki. When reading, you just have to figure it out from the context!

Why does مرحبا end with an "a" or "an" sound when I hear it spoken?

The word مرحبا is typically pronounced "marhaban". That "an" sound at the end is a grammar marker called "tanween" and is usually written as two small diagonal lines over the last letter (مرحباً). In casual writing, those double lines are often left out, but the pronunciation stays the same.