I understand what blondeangel means, but I do I get what you mean more Sarah.
My parents did this for me as my.. ahem "father" had nothing to do with me, where as my Dad has been in my life forever.
I never felt as though I lost an identity because it was never an identity I ever knew. If anything, I was embarrassed that somewhere out there, there was someone I was related to who wanted nothing to do with me. I have since met that man, and he has since died, but my Dad is still around, and I am so so so happy to have had his name until the day I married.
Sorry I am of no help to you. If your child already goes by your DP's name, and lives with you & your DP, I don't understand why your DD wouldn't/couldn't be regarded as a dependent (she is dependent on him right?)
Urgh... the system bugs me sometimes!
All the best hun