@Alexander Gomez , Based as i know, if both SQL server and VMM server are running on the same machine, renaming the server may cause the failure of starting VMM service. So we suggest to schedule a non-business time to do this.
As a reminder, please also ensure we have done backup before we take any action.
To rename the VMM server name, we can refer to the following steps:
1, Uninstall VMM server with "retain database"
2. Rename the computer name and restart the computer
3. Rename the instance of SQL server by using the following commands.
For a renamed computer that hosts a default instance of SQL Server, run the following procedures:
sp_dropserver <old_name>;
GO
sp_addserver <new_name>, local;
GO
For a renamed computer that hosts a named instance of SQL Server, run the following procedures:
sp_dropserver <old_name\instancename>;
GO
sp_addserver <new_name\instancename>, local;
GO
4. Restart the SQL service
5. Re-install the VMM server
Hope it can help.
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