My name is Noelle, and I was not born around Christmas. I didn't like my name very much when I was younger, since it was so different from everyone else in my class. Now that I'm older, I love it, and it always is a great ice breaker when meeting new people.
To anyone who speaks french or is familiar with Noel meaning Christmas in french the association between Noel and Christmas is obviously huge. That being said I think it would be ok to use Noel but spelled Noelle if it's for a girl. Noel pronounced either as Noll or No-el is masculine. Congrats!