At 9, I’d let her pick it herself.
Jack, I vote Jack.
Daria
Domenique
Ciara
Scotia (I have a relative with this name. It’s pronounced the same as in ‘Nova Scotia’. Very cool name.)
Natasha
Danika
Laina
Doesn’t “Regina” rhyme with “vagina”? 
For some reason I thought he was just rounding up some names he liked before presenting them to his daughter for the final decision.
Or are you having the final say, Roger?
She’s 9?
How about getting a baby name book from the library and going through it together? That way she can have a lot of input on her new name.
I am assuming that you are an Englishman living overseas so:
Frederika (Freddy) Flintoff Thornhill
Nine years old? What are her own ideas?
It’s my theory that every girl should have three names.
One ordinary, average, I-don’t-want-to-stand-out name that’s bully- and ridicule-proof, for school usage and in the office. Jane, April, Britney, Natalie, that kind.
One extravagant name that makes her feel really special, reflects her own tastes and that she can use in puberty or if she gets to work as an artist. Think Starchild, Willow, something Celtic or Welsh, native Indian, Spanish, or whatever your ancestry or her interests suggest;
And one ancient name that connects her to a (great)-grandparent of the same name. Beleulah, Anna, Elisabeth…the older and more European sounding the better.
Here, here! I second that.
And nothing whimpy like Jackie or Jacqueline, but a nice solid Jack.
You’re taking the piss out of the Americans on this one, aren’t you Roger?
Uran–that’s Japanese for “Uranium”, and also the name of Astro Boy’s “little sister”. 
Consider other Asian names as well. “Minmei” means “bright & beautiful”.
“Tomoe” is the name of a very brave & valient female Samurai.
Look at her features/hair color/attributes.If she is a runner/jogger, “Atalanta” would be good.If she has black hair, “Raven” would be extremely cool. If she is a good scholar, or likes to read, “Hypatia” would be good.
Consider girls’ names from Roman history, too.
When I suggested naming my daughter Alice, everyone instantly said, “Mel, kiss my grits!” (roger, it’s a catchphrase from an old sitcom about waitresses.)
I like Catherine (but it must be spelled with a C) and Savannah.
I was going to skip this post, but then the roaring sound of the whooshing drew me in…
Fabrizia Renaldini (I’m Italian decent, I owe this to my mother)
Yahoo IMAOL MicroGates (Give it a minute, play with it, let it roll around your mouth)
Serendipity Breeze (need I say more?)
A complete list, something for everyone, if I do say so myself.
Why don’t you email all the big companies for sponsorships? She’d get a new name, you’d get a million dollars, it works out great on all sides!
Except her new name would probably be something like Quicken Loans Thornhill or Wal*Mart Sam’sClub Thornhill.
E.
I’d say keep Natalie as an (unused) first name and call her by the middle. Saves legal trouble and potential clerical mixups.
James Lileks named his girl Natalie Claire. I like the sound of that.
Claire’s a classic, especially if she’s pale-skinned with huge luminous eyes, like Danes, Forlani or Bloom.
I’m taking a real shine to “Sally” lately. “Sally Jo” was my best friend growing up.
Keep Natalie for the first name.
Add Bathsheba for the middle name.
Think of the nickname potential: “NattyBats”, “Natsheba”, “Nataleeba”, “NattyBatty”…
Hey, what do you expect from someone who publicly refers to the kids as Dweezil and Moon Unit and at home calls them endearments like SmellyBelly and Stinkerbell?
Don’t forget Claire Fisher (dunno actor’s real name) from Six Feet Under…and Claire from The Breakfast Club (oop, there goes the luminous eyes bit…)
Hmmm. A new name for Natalie.
Hows about Eleanor? Love that name–and so unusual, too.
Or…
biblical names, religious names from other religions (Cali?), names of qualities like Sterling or Rockhard (well, maybe not that one). I just met a woman named Cyrana (seerahna)–I think it’s lovely. Supposedly, it’s the female version of Cyrano. Shakespeare is a great inspiration–Natalie Viola/Natalie Juliet/Natalie Beatrice/Natalie Ophelia/Natalie Hamlet (like that one).
Names you want to avoid–anything that sounds like it will end up in the trailer trash soon. Names like Tiffany, Brittany, Jasmine etc --read Freakonomics to get a true understanding of what I mean.
Historical references–middle name Hawthorne–hee hee.
Ok, am giddy now and must stop…
Will you post the final answer?
Bites When Provoked
It seems everyone has ignored the truly important part of your post, myself included. My apologies. I mean the kid will eventually just call herself whatever she wants. (Princess Jasmine is free now, by the way, as my daughter gave it up some years ago.)
Now onto the camera. Horatio, obviously.