SQL Server doesn’t support renaming the instance name directly. To work around the issue, you could use one of the following workarounds:
a) Uninstall the existed instance and install it with the new name.
b) Change the computer name and 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.
For a renamed default instance, run the following procedures:
sp_addserver <new_name>, local;
GO For a renamed named instance, run the following procedures:
sp_addserver <new_name\instancename>, local
How to: Rename a Computer that Hosts a Stand-Alone Instance of SQL Server