Is it possible to move this ticket purchase over to a new constituent with their biographical information?
It is currently not possible to simply transfer the ticket to another constituent record. A possible solution would be to cancel the ticket on the original constituent record without refunding the transaction. Then, you could register the new constituent to the event under a free ticket type. You will not be able to transfer the ticket transaction to the new constituent record, but this would allow you to keep the funds and simply register the correct constituent to the event.
To cancel the tickets and keep the funds:
Content > Events.
Select manage next to the event.
Search for the constituent name.
Select Cancel Tickets next to the constituent's name.