The name change doesn't matter.
If you mean that a customer had an open invoice on June 30, but is has been paid since, then by default the invoice won't show up on the report, because it is current paid off.
If you want transactions to appear that are currently paid off, but were not on the date of the report, there's a setting you can change to make that happen:

You you pick Report Date as shown above, transactions after the report date are magically backed out of the data and invoices will appear with their balances due as of the report date, even if they are paid on a later date.