I am not sure about the 'ACKOFF' spelling, but I've been told that the "ACOFF" surname is a combination of Russian/German/Hebrew descent. The '-off' suffix of this unique name is Slavic in origin so perhaps you may try searching the European surname databases. I have been unfortunate in my efforts thus far, but maybe you can turn up more. The one thing that is apparent however is that this name is extremely rare. There is quite a population of 'ACOFF's' in Canada; maybe there you can find a lead on the 'ACKOFF' spelling! Good luck and I hope to have been some help!