For some reasons, I cannot connect to my SQL Server with full name + instance name (e.g. server_name\MSSQLSERVER) by SMSS. However, I can connect by simply using just server_name or localhost.
When I check SQL server configuration manager, I did see my sqlserver is running with "SQL Server (MSSQLSERVER).
Best Answer
The default instance servicename is MSSQLSERVER, but the instance name is empty (just the servername).
This may occur (rarely) when you are not using the SQL Browser Service and are running on a non-standard port; in that case, the instance name alone is not sufficient to reach the instance.
A non-default instance has the Windows service MSSQL$INSTANCENAME; the default is (oddly) MSSQLSERVER (no $).