Fail-over or switching the Reporting server database I have two databases in server, dbs-01.One is a transactional database and a reporting server database.Reporting is minimum,that is why we have it together in the same instance.

I have transactional replication set to replicate the data from server dbs-01 to dbs-02.Currently i am replicating only the transactional databse only.

I want to replicate the reporting server database also which i can implement.
But my questions is :
If i want my application to point to dbs-02,i can do that my changing the connection strings in the application.
But what about the reporting server database.Because we have the Server Name in the Reporting Services Configuration Manager as  shown below(as dbs-01).

If my dbs-01 is down and my application is pointing to dbs-02 , how can i make the reporting services to work from the dbs-02.?

I am not an application developer so i am not aware of any settings which will help to make that switch.
Also configuring Reporting services for dbs-02 from the scratch is not a solution i am looking for.
You can use AlwaysOn Availability Groups to replicate the SSRS Databases to other servers, and reference the Availability Group Listener in place of the server names to allow for failover between servers.

Be aware that Availability Groups do not replicate server level objects such as logins or jobs. If you have any subscriptions in SSRS these will be scheduled jobs that will need to replicated outside the availability group, and you will need to put a mechanism in place to stop them firing when their server is not the primary node.

Here are a number of blog posts that go into further detail about setting up SSRS onto an Availability Group:
https://marcosfreccia.com/2018/06/25/reporting-services-databases-availability-groups/
https://jbswiki.com/2017/09/06/reporting-services-using-alwayson-availability-group/
http://techtalklive.org/ttlblog/making-sql-server-reporting-services-highly-available/