Skype for Business, Change display name on role-based account
The display name in Skype for Business uses the display name attribute in Active Directory. Your department's staff IT should have administrative permissions to the Active Directory OU needed to change the display name attribute in Active Directory. Once your IT pro makes this change, you should notice the change in Skype for Business within a few minutes to an hour.
This page describes how to change the display name for a role-based account in Skype for Business
For IT Pros:
The display name field can be changed by logging in to Active Directory Users and Computers (ADUC) and selecting "Rename" for the relevant AD object.