Need advice on a name for a character in a new story...

So I've had the song "Once Upon a Time in New York City" stuck in my head for months. For those that might not know, this is the song that opens Disney's movie "Oliver and Company".

After having the song stuck in my head for months I finally sat down and listened to it again. Now it's kind of inspiring me to write a story slightly based off the song, but more just inspired by it.

I've got the basic design of a main character set up. My dillema is that I'm kind of wanting to call them Oliver... It's a girl though... (I have a tendancy to want to name female characters traditionally male names.)

Do you think it would be weird to name my female character Oliver?

Do you think it would be tacky to name my main character Oliver at all since this song is generally associated with the movie "Oliver and Company"? (My story isn't really going to have anything to do with the movie. I'm just using inspiration from the song itself.)

Advice would be appreciated!