No, you can't rename the named instance.

BOL:

They can be used only to rename the part of the instance name that corresponds to the computer name. For example, you can change a computer named MB1 that hosts an instance of SQL Server named Instance1 to another name, such as MB2. However, the instance part of the name, Instance1, will remain unchanged. In this example, the \\ComputerName\InstanceName would be changed from \\MB1\Instance1 to \\MB2\Instance1