Yes, oddly enough both the witness and the transcriber got it wrong. According to other records, including her father's will, her forename is Mary and Ann is a middle name. I presume that she was always called by both names and therefor came to consider it all one name.
This illustrates my concern about transcriptions v the real document. It's the little nuances that get missed and, of course, the window for human error. I have heard some people say they've seen originals on the site and I wonder if the location is a factor with the Northern Ireland records being held by HM government. However, you have soothed some of my initial reluctance to accept that site's evidence.