Hi Lee,
Just to add to Helen's response ... it needs to be changed at a higher level than Moodle. So, for example, if you are using Office 365 to log in to Moodle, it needs to be changed in Office 365. Moodle is the downstream system. Until it is fixed at source it will keep being overwritten. Your institution might allow you to change your display name at the source but it is quite likely that you will need someone who is an administrator in that higher-level system to change it (usually someone in IT support).
Just to add to Helen's response ... it needs to be changed at a higher level than Moodle. So, for example, if you are using Office 365 to log in to Moodle, it needs to be changed in Office 365. Moodle is the downstream system. Until it is fixed at source it will keep being overwritten. Your institution might allow you to change your display name at the source but it is quite likely that you will need someone who is an administrator in that higher-level system to change it (usually someone in IT support).