Since the buyer sent payment to the wrong person base on the information you provided, we consider the buyer to have paid at this time.
If the buyer cannot recover their payment, you would have to either provide the account or issue a refund. Since they already have the account, it would be considered resolved.
If the buyer CAN recover the payment, then they should send it to you.
I recommend giving the buyer another 24 hrs to see if the person issues them a refund. If not, the buyer will have to open a dispute to recover it. That will take a few days to complete, then hopefully the buyer can send you payemnt.
If the buyer says he can't get a refund, I recommend asking them for video showing the original payment and proof they open a dispute via the Resolution Center on Paypal. You can then confirm if they were able to get their money back or not.