It seems you are trying to pass data from on-prem data with a private IP to Azure Storage.
We normally add the IOT devices through device connection string or X-509 or symmetric keys to destined Storages
But it won't be straight forward as you have private IPs on your Prem IOT device so you would be needing to secure your storage and IOT Hub with private endpoints.
and setup a conditional forwarder or DNS resolver on prem-DNS server to foreword the queries to Azure DNS server to look up private Ips for respective storage and IOT Hubs
You also need modify to outbound traffic in your NAT Gateway or Network security group or firewall to allow outbound connection to Storage and IOT Hub private IPs.
Once DNS resolution happens on storage and IOT hub with outbound traffic allowed on your on prem NAT Gateway, you send traffic to destined storage
Sample Diagrams from on Prem IOT to Private Azure Storage
Sample Diagram on Custom DNS from Azure ML (for Explaining DNS server and conditional forwarding to Azure DNS server)
Reference
Route data from IOT hub to storage
Custom DNS for Azure ML (for understanding on prem DNS server and conditional forewarding)
Troubleshoot connection to devices
Hope it gives the needed clarity on routing query from devices with on prem private IP to Azure private resources.
Thank you