I know this isn't exactly what you're looking for, but it will at least group by customer name.

Create a Custom Transaction Detail report.  Select the columns you want to show, as well as the Aging column.

Choose Transaction Types of Invoice & Credit Memo.

Group by Customer Name.

This will have your aging days next to each transaction.  You can also sort by Aging, either highest to lowest or lowest to highest, but within each customer name.

I think this is the closest you're going to get to what you're looking for in QB Desktop (Enterprise, Pro, Premier, etc.)

Another option is to use the Collections Report, where you have the option of choosing the number of past due days you want to show on the report.  If you want to see everything, then enter 0 days.  Then you will have a report much the same as the custom Transaction Detail report outlined above.

Good luck!