interesting website too.
From this it is clear that the person taking notes from the grave marker saw Willet as a middle name and did not identifiy a hyphen. So I am inclined to think it a clear error on the other site. This site also records the name as Adye not Ayde, unlike the other site. So, it would appear that it is in error on this count as well.
Both websites record Willet with a single T so I inclined to think that that is indeed how it is written on the grave marker, regardless of how the name appears in his book or the Army Lists.
Agreed that people are more exact in spelling today than then. It is a natural by product of how our IDs are tracked and used that precision is necessary today. Cheers,