A connection was successfully established with the server, but then an error occurred during the pre-login handshake. (provider: SSL Provider, error: 0 - The certificate chain was issued by an authority that is not trusted.) (Microsoft SQL Server, Error: -2146893019)
1) You might explicitly use "np:"prefix which ask for connect through named pipe and specify FQDN/LoopbackIP/IPAddress as server name in the connection string.
2) You might use FQDN/IPAddress/LoopbackIP to connect to the server.
To resolve 1) and 2), you can specify <machinename> instead of FQDN/IPADress/LoopbackIP.