Filing For Child Support For A Teenager For The First Time

This is a doozy, but I'll try to keep it brief as brief as possible.

TL/DR: teenagers are expensive, she has a good life, but child support could give her the extras she's craving. What are the risks? What are pitfalls? Could it be worth it?

I had a baby 14 years ago. She's my world, I love being a mom, and have been fortunate enough to have a solid middle middle class lifestyle. But, the cost of things like summer camp, sports, and activities as a teenager are starting to overwhelm me, and before I start issuing blanket no's to things she cares a lot about, I thought I'd investigate child support possibilities.

Here's some facts-

• This was fling, so we were never married.
• We live in OH and he lives in WA, but DD was born in a completely different state.
• No legal action has been taken so far- He's not on the birth certificate, and there's no custody or child support order in place.
• Paternity hasn't been legally established, though early on we did an independent one that was conclusively positive.
• He's seen her one time, when she was a toddler. He's not a terrible guy, but wasn't ready for parenthood. I've never denied access, but haven't heard from him in years. I've tried to reach him to work something out to no avail.
• He's not from the US but is married to an American, so I'm not sure of his status. It's all above board as far as I know.
• I do have an address for him, but have no idea where he works or how much he makes.
• She goes to good schools, gets good grades, we're active in the community, our home life is stable, and I'm a good mom- so I'm not worried about my parenting being questioned even if he wants to push it.
  
• She's the only child for both of us. I've never married, and have been mostly single since she was born- focusing on being a mom and growing my career.

Here are my questions:

• Right now, he's not on the Birth Certificate. Will he be added if we establish paternity and support? That would have to be done in the state where she was born, right? Do states automatically send that sort of thing to each other?
• Can he compel me to change her last name (she currently has my maiden name, and the same last name of my family (her village)). I don't want her to feel alienated by a sudden, unwanted name change. If he wanted to try this, he'd need to file in her birth state?
• I know that he could have worked to establish parental rights without my consent, but so far has chosen not to. If this action triggers him to file for visitation or custody, would he have a case? He hasn't shown any interest or support in 12 years, which I can't imagine would help his case.
• Will the courts consider her age and wishes?
• Is it even worth it? Are there risks I'm not thinking about?