To access the Redis instance via the normal hostname with the private IP, you'll need to add a custom DNS entry that maps the Redis instance hostname to the private IP address of the Private Endpoint.
- Get the private IP address of the Private Endpoint.
- Create a DNS A record mapping
my-instance.redis.cache.windows.net
to the private IP.
This will ensure that when you use the hostname, it resolves to the private IP within your virtual network.