My "name" is showing up as being my child's name when I text a friend

I have an iphone, an apple ID, a phone number. My daughter has an ipod touch, an apple ID of her own, and NO phone number. Because a phone number has to be used to create an apple ID, i used mine, and am her "trusted contact" for if she gets locked out.

Multiple people have sent me a message saying when they text me, my daughter's first and last name shows up as if it is her texting them. I've looked in all areas of contact cards, etc, and I can't find anything linking her name to me, except the fact I used my phone number. Help?? I don't want everyone thinking my 9 year old is texting them.