Our system uses email addresses to recognize users or customers. If a user is first created with a particular email address and name, all future ticket purchases using that same email will use the original name. This is because our system sees the email address as the most important detail about the user, and ignores any new names entered later.
To fix this, the event host or someone with admin access to the customer in the backend can find the customer in our system and update their name to the correct one they want to use. See info about how to edit a customer in this section of the "Manage Orders" options: "Names on tickets"