RBAC role to manage single pod with dynamic name
In Kubernetes, pods are considered as an ephemeral "cattle", they come and go. You shouldn't try to manage RBAC per pod.
In your use case, there is unfortunately no way to grant a role over a set of pods matching a certain name, because the resourceNames field doesn't support patterns like prefixes/suffixes. Don't get confused: a single asterisk character ('*') has a special meaning that means "all", but it's not a pattern. So, 'my-app-* in resourceNames will not work. There were tickets opened for this feature, but it wasn't implemented:
https://github.com/kubernetes/kubernetes/issues/56582
There was also a request to be able to manage RBAC over labels, but that feature isn't implemented neither:
https://github.com/kubernetes/kubernetes/issues/44703
Therefore, you probably need to change your model to grant roles to users to manage all pods in a certain namespace. Your deployment should be the only "source of pods" in that namespace. That way, you will not need to specify any resource names.