G'Day IJ!
An AOC is normally issued to ABC Pty Ltd, trading as XYZ Air Charter. As ABC Pty Ltd is the legal entity, that is the name one would expect to find in the CASA AOC listing.
For example, do a CASA search on the name "QantasLink" - no AOC in that name! But you can search and find the AOC's issued to "members" of the QantasLink group, SUNSTATE AIRLINES (QLD) PTY LTD trading as SUNSTATE AIRLINES for example - but still no "QantasLink"!
Knowing CASA's policeman in South Australia, I think it extremely unlikely the operator mentioned above would be openly advertising and operating
without an AOC.
