This name is horrible... only people who likes Halo can like it.
I mean, Im sure not everyone who have a Windows Phone plays or even likes Halo. In my case I only played Halo 2 and it was boring to me, so I didn't even know this Cortana existed. I don't even know how it even sounds like, of course I don't even care about looking it up.
now reading the name is really dumb and horrible, and it even sounds like Cortina (curtain if you need a translation) and sometimes it makes me think of Cortesana (prostitute), I know for some people it might be cool, but what about the people who don't even know this Cortana exists? what about the people who don't even know Halo exists? is this the right name for a WP feature that is in the hands of people who don't even know about Halo, dislike halo, hate halo, don't play halo?
I will not say Siri is a great name, its really stupid as well, but at least its easy to remember it and say it, unlike cortana. I would rather call this feature Taco, it wouldn't make sense, just like cortana, it wouldn't make you think about voice, like cortana. BUT it would be easy to say, and remember, and of course it would make you think about nice things, not a curtain or prostitute! (in my case of course)