An Irish surname, original form being ohEaghra. Many other variations of this name are Hara, O'Hara etc.
It can also be quite amusing when people are afraid to actually say O'Hora and are convinced you've got your own name wrong.
Person: "Oh, O'Hora is it?"
O'Hora: "Yes. O'HOra..not O'Hara"
Person: "Hmm, you don't hear that name everyday..."
O'Hora: "Actually I do."