How do i change my daughters last name to mine?

You follow the same procedures as an adult, he will have to be notified, and he can object. If he does object, the court will decided based on your reasons and the father's reasons not to change.
He is legally responsible for child support, and is the father, whether he is paying or not. I am curious, why do you not have parenting plan ?

His name is not on the birth certificate and i don't know where he is.

Ok, now I am really confused, if he is not on the BC, why is she using his last name? Did you apply for her social security card? How did you explain the last name to SS? without it being on teh BC?

You can name a child anything you want, so you have no problems in the beginning. Google search name change with the name of the state like this:

Texas name change

You will see the forms and the charges. It is pretty easy and cheap to do.

What I am attempting to determine, is whether she actually needs to petition for a name change, and how the child came to have a name different than her mother, when there is no father on the BC.

Children generally must have both parents concur in the change of their name. You must file your petition in the county/state in which you currently reside. . For the requirements for the change of name of a child see SUBCHAPTER "A" of the Family Code under Texas Statutes § 45.101(a).