My grandparents name was Yanke. One ‘e’ at at the end of the name. My grandfather was of northern German origin, from Breslau, in what is now part of Poland. I offer this as a point of information, no more.
Link to the column in question: What is the origin of the word "Yankee"? - The Straight Dope
As least, I assume that’s the column you’re commenting on? If not, let me know and I’ll provide a correct link.
As I understand it Janke is most probably a diminutive of Jan (=John).