If you come across a female ancestor described as “[Surname] alias [Surname]” in the parish register, you should certainly not assume that your great-grandmother led a double life, or had some sort of involvement with the cloak-and-dagger world of international espionage. While we now tend to think of an “alias” as a false name assumed for dubious, if not criminal, purposes, within the context of the parish register, it meant nothing so exciting or intriguing as that. It just meant “otherwise,” or “otherwise called/otherwise known as,” and was a way of recording a woman’s name with reference to both her family/maiden and her married surnames.
From the parish register for St. Michael’s, Corkery (Huntley township, Carleton Co., Ontario), the burial record for Margaret Jamieson, widow of James Moran, listed here as Margarette Jameson alias Moran. She died 12 July 1882 (her Ontario civil death record lists the cause of death as “Weakness”), and was buried at St. Michael’s RC Cemetery at Corkery, Huntley township on 14 July 1882, with her sons Thomas and Alexander Moran serving as burial witnesses:
The inverse of “[Family or Maiden Name] alias [Married Name]” is of course “[Married Name] née [Family or Maiden Name]” (which in the above case would be Moran née [born as] Jameson), which is the formulation that you will probably most often see.