This is so others reading this can use this solution to change the FullName in CRM Online.
So in my case, where I needed to change the FullName of existing CRM users from "First Last" to "Last, First", I was able to perform regular Office 365 admin functions to complete this.
First, I changed the format in CRM Settings > System Settings to "Last Name, First Name".
Then, for each user I needed to have changed, I used the Office 365 Admin Center and edited their licenses. Un-assign the CRM license from the user and click SAVE. Wait about a minute or two for the changes to take affect. Next, go back into that same user management and re-assign the CRM license to the user, click SAVE. Wait a few minutes and you will see the FullName in CRM should be in the correct format.