So my daughter is almost 15 months, and I've been taking care of her on my own. Her father will take her if I ask if he wants her for the weekend but usually leave her with his mom. She has his last name, but I want to change it to mine because I'm the one whose taking care of her and always will. There is no guarantee if he's always going to be around and I don't want her to b confused. How do I go about giving her my last name?

You have to go to court and request the change, but if the father doesn't agree its unlikely to be approved.

What if he's not on her birth certificate?

Does not matter, merely not being on the birth certificate does not take away his rights as the bio father.

Have you filed for custody and do you have a child support order in place and is there a court ordered visit plan ?

But in any regards, yes the bio father will need to agree to the name change and/or have the court approve the request

Since you gave her his last name, even if he isn't listed, the court will require that you identify the father and get his permission.

No. We just agreed on every other weekend. And I pay for mostly everything, even when she goes over there.

Since there is no court ordered child support ( from what I assume you are saying) he is not even behind on any payment, So he does not owe you anything at this point.