This has proved to be quite a problem which hasn't been conclusively answered yet. I had a word with Brian Austin who had no other reference to St Stephen's Square other than the 1861 census. Looking at the residents said to be living there in 1861 - I checked to see if any were still in the area in 1871 and found the HEWLETT family living in Taner's Buildings in 1871. We think that these were between Alma Street and Alfred Street - probably towards the Meadow Street end but have no proof that they were previously called St Stephen's Square.
Not much help here Kirsty. Do you have an interest in anyone living in St Stephen's Square in 1861?