I have an Azure Functions QueueTrigger that listens on a storage queue for messages like this:
Message text
--------------------------
{"ClientName": &q
According to the description of your problem, you do not need to concern about the message accumulate. And you do not need to create another function to listen on the same storage queue. If you use consumption plan for your azure function, it will scale out more instances to deal with the messages. You can refer to this document.
===============================Update================================
According to your requirement of each instance running may use up to 1 GB memory, I suggest you to use "Premium plan" for your function.
When you create function app with premium plan, you can choose "EP1" as below screenshot. "EP1" plan has max 3.5GB memory, so it can scale out to 3 instances when the function running.
After the function app created, go to the function app and click "Scale out(App Service Plan)", then set "Maximum Burst" as 3
. It means the plan will most scale out to 3 instances.
If you want more instances to run at same time, you can also choose "EP2" or "EP3" premium plan for your function app and change the value of "Maximum Burst".