I hope you're still getting posts in response to your 2008 post about the origin of the surname "Anckonie." It is either Lebanese or Syrian--I forget which at the moment. Alex Anckonie was a distinguished US naval officer who pioneered nuclear submarines under Admiral Hyman Rickover. There is info on him at the Arab-American Museum, in Dearborn, Michigan; they can probably give you some info by phone.
The two different spellings are of no consequence. There was no standard way to convert a foreign name into the English alphabet, and still isn't, really.
You didn't find any hits when you googled "Anckonie"? Curious, unless no material on Alex had yet been put on the Web...