I’ve always thought that dator was just a short form of datamaskin. But some other comments suggested otherwise, so I had to look it up. Apparently, dator is a made up word from 1968, from data and parallels the words tractor and doctor.
Yes, it's "dator". The word was initially proposed based on the same Latin -tor suffix as in e.g. doctor and tractor, so the word would fit just as well into English as it does in Swedish.
