The reason why William H. Fisher, and many other members of the 47th Arkansas (indeed of all the other 40-series regiments as well) is that no muster rolls were ever submitted to Richmond. The only documented names are those taken from U.S. prisoner of war and parole records, and a few quartermaster receipts. That leaves a whole bunch of people whose service cannot be documented in the CSRs. Postwar pension records cover some of them, as does the occasional postwar narrative and local history.
I've spent more than 25 years putting together a database of all known Arkansas Civil War soldiers, Confederate and Union, which makes it possible, in most cases, to distinguish between soldiers with similar names. Most researchers have been on wild goose chases at some time or other, and my database helps eliminate that aggravation. If I'm asked to list all similar names, I am, of course, happy to do so, but most researchers want to focus on the actual soldier they're researching, so that's how I respond.