The following is a transcription of the script and a few screencaptures of the trailer which was shown for Devil May Cry 4 at the Tokyo Game Show 2006.
There hasn't been a officially released fort he girl's name is.
( Yay her name IS Kyrie!) - However, when I listened to it I heard "Kyrie" each time. I heard "kee-ree-ay" and coincidentally that is the same way "Kyrie" is pronounced. I asked 4 other people to listen to it multiple times and they heard the same thing. It would make sense logically if her name were Kyrie because both the name and she has something to do with the church. However, it would be very odd to have someone named "Kyrie".

  ± Devil May Cry 4 Trailer Script
Kyrie: Nero!

Nero:: Kyrie... KYRIE!

Dante: Do you really think you're a match for me? Then show me. Let's play! A little refinery now and then does make life more interesting. Don't you think?

Nero:: Now I know. This hand was made to send guys like you back to hell!

Dante: Return it to me, and I'll let you go.

Nero:: TRY THIS!

Kyrie: What did I tell you before? You know you're you. It's you I want to be with. I don't know anyone else who is as human as you are.

Nero:: From that day forth, my arm changed. And a voice echoed. Power....give me more power!

  ± Devil May Cry 4 Trailer Screencaptures

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