E.H.
It is not hard to change your name when you get married because it is the traditional way of things so getting new id is not hard at all if you decide to do that and take a marriage license with you. Your child is another issue. Unless the biological father signs off on a name change of the minor I don't believe it is possible until she is 18 and can do it herself.
I know that if you want to change your name in Porter Co IN you need to pay a fee and do some paperwork, then put an ad in the paper to give people a chance to protest the change. If nobody objects to your change, you are granted the name change. This might work for a child, but I don't know. I only know this because my husband was going to take my maiden name as a middle name (like our children) to have a special family name thing. But this was all too much hassle he said.
Oh, and don't know if you remember the OC but the one women on there had like 3 last names from getting divorced and remarried. Now it is not strange at all to have different names in a family.