I think it comes for Aduke. Here is a quote from Meet Addy
"Your great-grandma's name was Aduke. That name got a meaning where she come from. It means 'much loved.' I saved that name for you Addy."
<font size="2" face="Verdana, Helvetica, sans-serif">It's definitely short for Aduke.

Personally, I didn't think that quote was enough proof, it could have been that Addy's mom liked the name, but wanted to name her daughter Addy instead of Aduke, meaning her full name was, indeed, Addy.

However, it says in the Peek into the Past, "For example, Addy's whole name, Aduke, came from Yoruba, one of the languages of West Africa, (Meet Addy, page 65)."

No, I'm pretty sure that name isn't shorted. Although there are 2 different ways of spelling it.
<font size="2" face="Verdana, Helvetica, sans-serif">If you mean "Addie," that would actually be a spelling error. It's never spelled that way in the books. Sometimes people just don't know how to spell it right, sort of like "Josephina." Which IS a name, but is not how our Josefina's name is spelled.