The server name, that you enter there is the name of the computer, on which the SQL Server has been installed. This is called "default instance", because you do not specify a name of the instance, which is in the format "computer_name\instance_name". If you are trying to connect to an instance (either default or named) installed on your local computer, you can substitute computer_name with . (dot), i.e. you can connect to a default instance on your computer by giving ., or to a named instance as .\SQLEXPRESS for example.
So in your case if you specify only a dot for server name, you should be able to connect. If you don't connect, then the SQL Server instance is not working. You can check is the service started, but you may have to reinstall SQL Server.
If the connection is successful, then you can keep using . (or (local)). If you want to find your computer's name, from Windows Explorer right click This PC and select Properties, then look at Computer name:.
If you still can't connect to the SQL Server using this computer name, then you have issues not related to the SQL Server engine itself. Open a command prompt and try to ping the computer name: ping desktop-7t2s4sm. If you get an error, then you have a networking issue.
