Personally, I doubt that readers care.
My business license and Chamber of Commerce membership are under "Umbach Consulting & Publishing" so I don't have to fool with a fictitious name statement. (It started as "Umbach Consulting," but I added "& Publishing" years later when I added book publishing to what I was doing.) I shorten that to "Umbach Publishing" for my books, and "Umbach Consulting" when talking just about services. The tax people don't care what I call it as long as I file and pay what I owe. (A CA Board of Equalization rep. told me so explicitly for sales tax & use tax purposes.) Some of the independent publishing companies I know locally are "Potts Publishing" (author/publisher is Bill Potts), "Bridge House Books," "Willow Valley Press," "Deer Valley Press," "Stagecoach Publishing," and "Great Little Book Publishing."
Considering the number and variety of book publishing company names, it is hard to think that publishing company name per se means a lot to readers. And consider the strangeness of some (Small Beer Press? Ten Speed Press? Health Publications, of Chicken Soup fame? And for that matter, Random House.)
My advice is to focus first and foremost on the systematic building of platform for yourself as speaker (scores or hundreds of appearances per year) and article writer (dozens per year), and consultant to agencies and organizations (several, if not a dozen or more, both private and governmental) and on the quality of the book itself. Without an effective platform the rest is going to waste anyway.
--Ken