There are some ebook and vanity publishers that market ISBN assignments using their imprint name. Although they probably do not have any rights, using another company's name injects confusion and can limit your ability to sell your books worldwide.
Our arrangement with the US ISBN Agency enables us to have clients either have "Independent Publisher" listed as the referenced imprint using our Self Publisher Package or an author/company name using our Publisher Package. Do not risk limiting where you can sell your books.