Though the approach I'm about to share is quite old, still it standsout among other ways, as it is easy and automative. Following is the set of cmdlets which are perform the required "rename" functionality:
//set the azure container
string blobContainer = "myContainer";
//azure connection string
string dataCenterSettingKey = string.Format("DefaultEndpointsProtocol=https;AccountName={0};AccountKey={1}", "xxxx",
"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx");
//setup the container object
CloudStorageAccount cloudStorageAccount = CloudStorageAccount.Parse(dataCenterSettingKey);
CloudBlobClient blobClient = cloudStorageAccount.CreateCloudBlobClient();
CloudBlobContainer container = blobClient.GetContainerReference(blobContainer);
// Set permissions on the container.
BlobContainerPermissions permissions = new BlobContainerPermissions();
permissions.PublicAccess = BlobContainerPublicAccessType.Blob;
container.SetPermissions(permissions);
//grab the blob
CloudBlob existBlob = container.GetBlobReference("myBlobName");
CloudBlob newBlob = container.GetBlobReference("myNewBlobName");
//create a new blob
newBlob.CopyFromBlob(existBlob);
//delete the old
existBlob.Delete();
Hope this helps!!
If you need to know more about Azure, then you should join Microsoft Azure certification course today.
Thank you!!