It's spelled Berrigan. I don't remember which ep it was, but there was an envelope addressed to her once, and it was spelled that way on it. I know the show isn't always consistent with the spellings (they once spelled it Caffery in a syllabus they used as a prop), but I think it's been more or less officially confirmed that it's Berrigan with an E. It's spelled that way on the official website too, actually.

LOL @ the Freudian typo. Loved your little pun-filled piece there. :-P