If you choose to get a custom ISBN to self-publish, you will become the publisher. You need to come up with a name for your publishing house. Take the time to put some thought into this decision because it will be branded with you forever. Don’t make it your name or the name of your book.
You may even end up setting up a separate website for your publishing house, so make sure it is an available name on the web and/or isn’t trademarked in a way that you would be breaking trademark laws.
Go to the Trademark Electronic Search System (TESS) to see if someone else has already gotten a trademark on the name you are considering for your publishing house. Once you look the name up in TESS be sure to do a thorough Google search to see if someone is using the name. Even if they have not registered a trademark they could still win a case against you base on their first right of use.
Selah Press is a publisher. If you would like to investigate having Selah Press as your publisher here are links to Selah Press Bite-Sized Publishing, Selah Press Publishing and a link to the submission form.