Update: There is now an option to use the pool-name as the worker-ID. I have updated the quickstart-instructions to do this automatically, i.e. if you create a new startup-script with the quickstart-instructions your miner will use the azure-pool's name as the worker-id.
 
If you are using my detailed-script, there are some variables which let you configure the worker-id any way you want:

• ${AZ_BATCH_POOL_ID}    : The name of the azure-pool used
• ${AZ_BATCH_ACCOUNT_NAME}    : The name of the azure-batch-account used
• ${AZ_BATCH_NODE_ID}   : The name of the azure-pool-node. Typically this is a complicated name with some special characters. Use at your own risk!

Just place one of these variables where you would normally put the worker-id, and when the miner is started it will get replaced with the corresponding content. You can have a look at the script generated by the quickstart-instructions to see an example for using the variable ${AZ_BATCH_POOL_ID}.