Although not a common surname in Germany, I've come across *Ade* several times in southern Germany and Austria. As far as I know, the German *Ade* derives from *a deo* and is essentially the same as the French adieu - all meaning *God be with you* or *to God*. In my region of Germany (Baden), where I grew up, a colloquial greeting for *good bye* is *ade* with the emphasis on the *e* rather than on the *a* which is how German-speaking people pronounce the surname Ade. (aadhe)
Other than in German-speaking countries, I have seen Ade folks from England - the writer and humorist George Ade, after whom a trucks stop in Indiana is named, is the most prominent English *Ade* representative.
Another place were the surname Ade appears is Africa, specifically the Ivory Coast. The most prominent one is *King Sunny Ade* a now deceased African jazz musician. I found out about the *Ade*s from that region of the world while working at the Munich Olympics.
So much to know and learn, so little time...