Robert, it is not only possible to change the last name, that is the prescribed way to correct a last name on WikiTree. We don't want to create duplicates - when we discover that they have been accidentally created then we have to merge them, but it is much better to avoid having to do that whenever possible.
The LNAB (Last Name At Birth) can only be changed by a profile manager. You can ask your cousin to add you as a manager (a profile can have more than one manager) and then on the edit page you will see a link next to the LNAB to change it. You could also ask your cousin to change it.
For the duplicate Hester Hodges profiles, if you scroll to the bottom on one of them, you will see a link you can click to propose a merge. If the correct name is Hodge, then you can change the name on one of them first, then propose the merge, making sure that the correct LNAB will be the resulting profile.