Generally, it's handled by the distro's package management utility. For example, if I examine the contents of
postgresql-libs on my desktop (Fedora 28), I find that:
[me@risby personal]$ rpm -ql postgresql-libs
and sure enough, therein it lies:
[me@risby personal]$ head -11 /usr/share/doc/postgresql-libs/COPYRIGHT
PostgreSQL Database Management System
(formerly known as Postgres, then as Postgres95)
Portions Copyright (c) 1996-2018, PostgreSQL Global Development Group
Portions Copyright (c) 1994, The Regents of the University of California
Permission to use, copy, modify, and distribute this software and its
documentation for any purpose, without fee, and without a written agreement
is hereby granted, provided that the above copyright notice and this
paragraph and the following two paragraphs appear in all copies.
This is equally true for packages that don't come from RedHat, but from a different repo;
rpmfusion-free includes the following files:
So you can see that although there's no standard name for the file, there's a standard approach to including it.
You're not planning on shipping binaries, you're planning on shipping an entire OS image, which is a slightly different problem. Personally, I'd encourage you not to do that, because more people will use your software if (a) it's easy to see exactly what they're installing, and (b) it interacts properly with everything else on their systems. But if you must, I'm sure you can find somewhere inside that image to package some text.