You can always change your name via your profile. Please note that if the Deutschlandticket was purchased via the hvv switch app, the name will be updated automatically when the ticket is issued for the following month.
If a driver's license validation exists, the name change will initially lead to the validation being revoked.
In this case, you can simply carry out a new validation with your updated ID document in order to be able to use the services requiring a driving license again without restriction.