it's pronounced literally the way it's spelled. Doherty. Daw-her-tee.
it's funny how english people usually complain about irish names NOT being spelled phonetically and then when they're confronted with one that is they make up their own various pronunciations of it. i'm guessing they stem from phonetic, mispronunciations of Docherty and Dougherty that have carried over even to the least complicated, most phonetic spelling somehow.