This page describes how to change the display name for a role-based account (RBA) in Skype for Business
The display name in Skype for Business uses the display name attribute in Active Directory. Your department's IT support should have permissions to change the display name attribute in Active Directory for role-based accounts (RBA). Once your IT staff makes this change, you should notice the change in Skype for Business within a few minutes to an hour.
For IT Pros:
The display name field can be changed by logging in to Active Directory Users and Computers (ADUC), getting Properties on the user object, and changing the field called "Display name".