"Excuse me, what is your name?"
打扰 is a verb which means to disturb, especially other people's life, work, routine or plan; So 打扰了 means "I disturbed you".
(BTW personally I think it's a bit awkward to use it in Duolingo's sentence. Usually we would say 不好意思 or 对不起).
打扰了 is best used in situations of receiving hospitality, e.g. when you enter a friend's house for a dinner treat, or for passing a weekend.
Of course, but you can't guess the meaning of a chinese character by how it looks, even more, you can't even know how to pronounce it, so, how are we supposed to know that 打扰了 is a valid answer? by pure guess?
I can't recognize or even spell any of those characters becouse none of them has been introduced on any lesson yet, so, am i supposed to get a correct answer by guessing? Even if i do it by chance, that doesn't mean that i've actually learned it.
Again, i agree with your statement, but not as a justification for this.
不好意思 bu4 hao3 yi4 si would be the right phrase to use if you walk up to someone randomly, an want to say 'excuse me' in that sense. 对不起 is used more as an actual apology. 请问 is a more general, polite way to introduce a question, and could be used in the middle of a conversation, not only at the beginning.