If that'd be so, it might come from a "make it sound and spell English" Goodenowe, Godunov, Gudanowski etc.
Lo-and-behold John Goodenough is from Thuringia, Germany, born to Jewish parents, father Erwin Ramsdell Goodenough. So quite likely the name was transcribed at some point in history, even if not documented in Wikipedia et. al. very publicly, we can see that his father in turn seems to come from said "Goodenows" via the references link in the father's Wikipedia page [1].
Just speculating, but -enau is a common town name ending in German, a person from that place might be name -enauer (see Adenauer). There is a Gudenau Castle in west Germany. Gudenauer would have been an excellent candidate for Ellis Island-fication
But according to the Wikipedia page John Goodenough's dad, Erwin Ramsdell Goodenough, was born in Brooklyn and the son of Ward Hunt Goodenough. The links suggest he stemmed from a family that emigrated to America in the 17th century.
All the above info I gave is from said Wikipedia page including the link. It's the reference (number 3) that the Wikipedia page for John's father gave.
I have not done any source work. I'm trusting Wikipedia here.
