I am having some confusion with a rent-to-owned property. The deed was transferred the day of closing and the funds of the loan were used to payoff an external institution's balance on the loan for the property.

If names were not the same on new and existing loans, this cannot be a refi correct? Would this be considered a purchase?

At least one borrower has to be on both loans (paid off and new) in order to be a refi. If there is no borrower in common, you are correct, it cannot be a refi.

You may need to check your state law, but if title passes to a new owner, we always call that a purchase. So if it was rent-to-own and the title to the property is passing to the renters now, we would call that a purchase.

Does the rent to own contract grant ownership to the "renter", does the contract constitute an extension of credit under state law?

An exert from page I-2 in the 2021 GIR.

2. Extension of credit. Under § 1003.2(d), a dwelling-secured loan is not a closed-end mortgage
loan unless it involves an extension of credit. For example, some transactions completed
pursuant to installment sales contracts, such as some land contracts, depending on the facts
and circumstances, may or may not involve extensions of credit rendering the transactions
closed-end mortgage loans.