Here is the same scenario what I am facing. Sharepoint 2013 - SQL Server connection stopped working shortly after database server rename.
Note! :- in my case automatically Central admin is not accessible and I tried the powershell command mention in the above question got below error on SP power-shell.
On event viewer i am getting this below error which is occuring every 46th second. Event ID:-5586 Unknown SQL Exception -2146893007 occurred. Additional error information from SQL Server is included below.
A connection was successfully established with the server, but then an error occurred during the pre-login handshake. (provider: SSL Provider, error: 0 - The client and server cannot communicate, because they do not possess a common algorithm.)
Event 5586 (SharePoint Foundation) of severity 'Error' occurred 46 more time(s) and was suppressed in the event log