The person I know with this name says it "uh-LEESH" like the American pronunciation of Alicia or Felicia, but without the a at the end. (I initially thought it was "Alicia" until I saw it written.)
My real name is Eilish, and it's definitely pronounced so that it rhymes with 'fish'. Although, my mum says that I pronounce it wrong. Plus, it is the best name ever.