Any idea how I can turn off/bring down primary Azure SQL database / SQL Server in fail over group to replicate an actual scenario like a data center is down? I tried renaming but doesn't work. All I am trying to do is take one of the Azure SQL databases offline in the failover group. Any ideas how it can be done please?
You can use a forced failover which may result in data loss same as a server down or datacenter down scenario. Note that is not the same as a manual or friendly failover using the portal, on which case there is no danger of data loss.
You can use REST API to generate a a forced failover as explained on this documentation.