Hello @Yanet Morales
Managed Identity is not integrated between Azure CDN and storage yet. Azure CDN Premium supports Private Link, which can be used to access storage privately.
Using Azure CDN Premium created, create private link service and WAF policy and select custom origin type and enable private link service like below:
Created a private endpoint in Azure storage account to access securely and select the pending private endpoint request from Azure CDN Premium then select Approve like below:
Once the Azure CDN created with host name storage account blob will access private blobs securely:
References:
Secure your Origin with Private Link in Azure Front Door Premium | Microsoft Learn