we have already seen in a number of threads that people were more flexible with their names then. Some examples include Senarmont with or without an accent, Davout or Davoust, Cook or Cooke.
We do know how his name is shown in his book. We have seen Adye as standard in the Army Lists, but it seems Willet and Willett both occur. The only instance of hyphenation seems to be on the gravestone, according to the website that Steve gave us.
Personally I'm done chasing this. I thought it an odd discrepancy when I queried Steve.