After many hours of research, discussion at the Rootschat forum (see A Harper Family Conundrum) and a substantial amount of head scratching, I believe that Wilfred Eric Harper was born William James Harper. The best way I can provide support for this conclusion is by noting the information that we have, in point form.
Wilfred Eric (aka William James) Harper
![5WilfredEricHarper_1875-1921 Wilfred Eric (aka William James) Harper](https://harperfamilytree.com/wp-content/uploads/2013/04/5WilfredEricHarper_1875-1921-e1402671649850.jpg)