SQL Server Certificate – Fixing ‘The Certificate Chain Was Issued by an Authority That Is Not Trusted’ Error

some time ago I installed SQL server 2016 developer edition on a windows 10 home edition environment (a laptop to be precise) and everything was fine.

then someone – an administrator on the box – decided without telling me, to rename said box.

after that when attempting connection to SQL server we have been experiencing the following error messages:

this is a very similar question to this one:

“The certificate chain was issued by an authority that is not trusted” when connecting DB in VM Role from Azure website

I have been also here:

The target principal name is incorrect. Cannot generate SSPI context. (Microsoft SQL Server, Error: 0)

and I have been using the Kerberos Configuration Manager, which gives me a different error message

I should say that I Am able to connect to this instance of SQL server by SQL server authentication but I want to connect using windows authentication.

just to be clear – this is all a local machine, that does not belong to any domain.

I am not quite sure as how to proceed from here, what I want is to use windows authentication.

The error message related to certificates makes me think about re-issuing certificates here.
I am not sure as for how to get this done, or if this is a valid way to go about this situation.

I will not be around this machine for the day, but I will catch up as soon as possible. I will carry on with my research when time permits.