How does SSMS connect to a server's database without the instance name?
For SQL Server the default instance of a  is SQLServerName\MSSQLSERVER.  However, since MSSQLSERVER is the default instance name that is never displayed.  

A SQL Server using the default instance is only referenced by the SQLServerName.

Actually, you can install SQL Server Express and give it the instance name of MSSQLSERVER and you will get the default instance.  Of course, any server can only have one default instance.  

That is probably most useful when installing a SQL Server Express and you do not want to have SQLExpress for the part of the name. 

When installing a default instance of SQL Server Express at the Instance Configuration page, you must choose the Named Instance radio button and type in the default instance name of MSSQLSERVER. 

Just take the steps to name the default instance name MSSQLServer (which will not appear).  Any other instance name on the computer needs a unique name, such as SQLServerName\Alpha, SQLServerName\Beta, et cetera.

Note: Installing SQL Server Express will, by default behavior, put the SQLExpress into the server name.  But that is not the default name. Whenever there is \Sometext name, then that is called a named instance.