I was in my 20's when I realized Bill and William are the same name

I read a lot of Enid Blyton in my youth; by ten I know bill/william and richard/dick, etc.

My wife had a grandfather with the first name Bill and middle William. After 12 years together, I'm still not sure if she's just messing with me.

Will = William

Ipso facto:

Bill = Billiam

Mutatis Mutandis:

Jim = Jimothy