Not unique. If you look at google, it lists ones named "The Why Not" at present (if not since closed recently) in Wolverhampton, Halesowen, Darlaston, Redditch, Essington, Astwood Bank and Wednesbury. Unfortunately, as you will have realised, the newspaper archive search omits some short words, so it gives many references to "why" , but ignores "not" . Tried looking for licensing applications around that time, but they were not well reported and could not find any for this name. Of the 14 licensed premises listed in the PO directory for 1849, only two are unnamed. (listed as beer sellers), no 145 occupied by John Parton and no 117. occupied by John Brown. The 1851 census shows no145 occupied by John parton ,listed as publican, and no 117 occupied by Joseph Tandy, retail brewer, but no name given in either case to the pub. (to me retail brewer suggests beerhouse rather than off licence) Was not able to check the 1862 census , as for that year Ancestry seems at the moment to only respond to names in wales and scotland ! There was a renumbering before 1871, so have not had chance to check the 1871 census