Local and Microsoft account name problem

Hi

I installed Windows 8.1 Update 1 Enterprise 64-bit.

I created a local account and I changed the name displayed in the Start screen.

Then, by this account, I performed the procedure to switch to a Microsoft account.

I noticed that when, by this Microsoft account, I perform the procedure to switch back to the local account, the name displayed on the logon screen, it is to be returned to the original one (ie, the one of the directory of the local user profile). How come?

So, how do I make sure that, at the end of these procedures, the account name back to being what had been changed by me?

Thanks

Bye

Balubeto