>I realize that the cryptic name (DESKTOP-VF4MCSR) I see in the SSMS is not the SQL Server name but rather my computer name. I Googled and found steps to change the computer name to something more meaningful.
>My question: if I change the computer name, will my SQL Server still work? What other parts of the computer may malfunction if I change the name?
>
>UPDATE: Changed PC name and the default SQL Server name is changed as well. No problem connecting.

Actually, the SQL instance's name is unchanged, it's still mssqlserver or something like that - the default. And that default doesn't need to be mentioned in the connectstring - it can be omitted and the clients will find it by issuing just the machine's network name. As long as you included the new machine name in connectstring, of course it connected.