When you publish through Amazon KDP, you can accept a free ISBN. If you do, the publisher of record on your book becomes "Independently published." That is what appears in Nielsen's database, in library catalogues, in Ingram's wholesale system, and on your copyright page. Not your imprint name. Not the name of the press you have spent time building. "Independently published."
This is not a hypothetical concern. Publisher of record is a real field in the systems that booksellers, librarians, and distributors use to evaluate titles. An ISBN assigned to your own imprint communicates that you operate as a publisher. One assigned to KDP communicates that you operate as an author using Amazon's infrastructure.
In the United States, ISBNs are issued through Bowker. A single ISBN costs $125. A block of ten costs $295, which works out to $29.50 each. A debut novel in standard formats (paperback, hardcover, and ebook) needs three ISBNs. The full cost of establishing your imprint as publisher of record across all three formats is less than a month of most professional software subscriptions.
What you receive in return is specific. Your imprint name sits in the publisher field in every system that carries your title. When a library orders through Ingram, they see your press name. When a retailer checks wholesale records, they see your press name. You can move your files between platforms without the ISBN becoming void. You own the publishing identity, not just the manuscript.
IngramSpark, unlike KDP, requires an ISBN you own before it will list your title. That requirement is not bureaucratic overhead. It is the infrastructure telling you that the distinction matters to the systems that handle your book once it leaves your hands.
The free ISBN is free in the way that any service is free when the cost is ownership of your own publishing identity.
Map's Edge Media ISBNs are registered to the imprint, not to any platform.