Today, I worked on a service request that our customer received an error message connecting from PowerBI to Azure SQL Database using Private Link.
The error message was: The server name provided doesn't match the server name on the SQL Server SSL certificate.
We found that this issue ocurred when our customer uses in the connection string the FQDN: servername.privatelink.database.windows.net instead of servername.database.windows.net. When the server recieves the connection the SSL certificate validate the name.
Our first suggestion was to use servername.database.windows.net because at the moment of the definition of the private link you could create a private DNS that will be added in your VNET/Subnet.
Other options are:
You could continue working even after the message, basically you could press OK and continue using PowerBI..
If your DNS didn't allow or you cannot add an entry in your DNS, you could add in the host windows file the entry of your server.