No.
I provide you with a list available domains names, but it's up to you to buy and/or register whichever you may want to use.
The available .com domain names that I locate for you may be unregistered in which case it will be easy, cheap and fast to register the name, or the name may be already registered to a private party who interest in selling it. Successfully completing a private party sale can be simple quick and easy, or it could become a real negotiating challenge and that all depends on who's selling it.
Unregisterd names can be registered quickly, easily and cheaply at any registrar like godaddy.com for a nominal yearly registration fee that's generally around $10/year.
Private seller domain name prices vary wildly, but often a few hundred to a few thousand dollars will work for a private seller.