Active Directory Name Change
SQL Server stores Active Directory accounts using a unique identifier generated by Active Directory.  The unique identifier is generated when the object is created in Active Directory, and never changes.
This means you can change things like the user name, first name, last name, and any other Active Directory attribute for the user, without the need to even touch SQL Server or SSMS in any way.
In other words, you can change their account name in AD, and not worry about SQL Server at all.