Determine what you want your brand to convey: What is your genre? Are you writing fiction or nonfiction? If you write mysteries, for example, are they funny or suspenseful? Under what category would your book be placed in at a bookstore? Who is your audience? The answers to these questions will determine what you want your brand to say. Your publishing company name will "brand" you in the minds of those who work with you. Branding applies more to booksellers and other distribution channels than readers, generally speaking.
Use a thesaurus to explore word variations. If your books are going to be "funny" or "quirky," try inputting those words into an online thesaurus to find words with similar meanings that you can consider. Try the word as either a stand-alone publishing company name, or with the word "books," "publishing," or "press" after it.
When you've picked a name you like, be sure no one else is using it. Do a Google search, using the entire phrase (if it's more than one word) in quote marks. The results will generally tell you if a name is being used or not. If nothing shows on Google, do one more check: Go online to booksinprint.com and register. This site lists every book in print and can be cross-referenced by publisher. Search the name you want to use by publisher name. If anyone in the US is using the name to publish books, they'll be listed here.
Make sure the domain is available. Before naming your publishing business or registering it anywhere, you need to know whether the domain name has already been claimed. Domain registry sites such as mydomain.com allow you to search for domain availability. Web presence is vital in business now and you want to own your domain.
Protect your name. Register your DBA (doing business as) name according to the local laws of your area. Register the top level domains (.com, .net, .org) for your business name. Do this immediately. If you wait, someone else could take it from you.