My ex and I had a child out of wedlock. I and the child now live in a different state and he has not had contact with either of us for 3 years. I want to change her last name to my last name since he is not in the picture. Is this a valid reason for wanting my child to have my last name?

How can I change my daughters last name to mine when her father has had no contact with her for over 3 years?

It is a reason to want to, but you still will have to get the "ex" permission.
You can, if he refuses, try to show the court, it would be a major benefit for the child. But it is not likely to happen without the father agree

How can I change my daughter's last name to mine if her fathers name is on the birth certificate but we were never married? Also, the state we live in collects child support whenever he has employment but it isn't steady and he owes over $6000 in back pay. He hasn't been in contact with her for over 2 years. I would like her to havemy last name since she lives with me and he obviously wants nothing to do with her. Is this even possible if I can't locate him?

Please stop starting new questions for the same topic, they have all been merged

You can file a name change petition in court. You will have to show a good faith effort to serve the father notice if you don't know where he's at. The child support agency may help serve him.

Whether the court will grant the name change depends on the local court. I do think it's a slim chance.