If you are given access to a SQL Server, how do you find if the SQL Instance is a named instance or a default instance?

I would go to the SQL Server Configuration Manager. In the left pane of the tool, I would select SQL Server Services, the right side pane displays all of the SQL Server Services / components that are installed on that machine. If the Service is displayed as (MSSQLSERVER), then it indicates it is a default instance, else there will be the Instance name displayed.