Read-Write permissions issue for PVC in Azure Kubernetes Service
Posting this answer as community wiki since it might be helpful for the community. Feel free to expand.
As mentioned by @Nick Graham in the comments
To modify the permissions on a mounted volume you’ll need to execute a script after the container starts up. Some images give you the option to copy scripts into a particular folder that are then executed at start up, check the docs to see if the image your using provides that functionality
There are few examples.
Additionally according to this comment you can try to specify this permissions in your storage class.