Ok, let me be clear: You cannot adopt your own daughter. Your DAUGHTER should proceed with a legal name change when she turns 18.
Exactly.
Just so OP knows the options, it IS possible to go to court to ask for a legal name change for a minor, but I wouldn't even consider it for a 17 year old for a number of reasons:
1. It will cost a significant amount of money for attorneys, especially if Mom wants to fight it.
2. It will take a MINIMUM of 6 months, maybe more - so it may not be done until after she's 18, anyway, so all the money will be wasted.
3. It will simply create one more thing for you and her Mom to fight about. I'm not above a good fight if there's a reason for it, but since there's no reason for it (see 1 and 2), why bother?
Wait until she's 18 and she can file for a name change. The County Clerk can probably direct her to the correct forms - or she can find them online. It will be a simple 'fill out the paperwork, submit it, and you're done' process rather than a battle.