Power BI report server points to Old database when automatic refresh kicks in

Hi,Mithraveer .Thank you for your reply.
Given that your situation is unique and your repot server version is May 2020. So I have found the following relevant documentation which I hope will help you.
URL:
Change data source connection strings with PowerShell - Power BI Report Server pre-October 2020 - Power BI | Microsoft Learn
 The reportserver version is very important, while changing your report server version is generally not recommended.
For your question: does the report server support editing your tnsnames so that it can also pick up hostnames.
The report server itself has a lot of limitations, so it is best to operate according to the official documentation itself to avoid data loss and other accidents. As for the report server's ability to recognize tnsnames, I suggest you contact your team's IT department and ask them to let you know if they are skilled in the use of power shells to avoid accidents.
You can try to modify the connection string of some databases to see if it works.

I hope my suggestions give you good ideas, if you have any more questions, please clarify in a follow-up reply.
Best Regards,
Carson Jian