In the United States, she was known as "Jane Garrow" and sometimes "Mary Jane." She was baptized, though, Marie Genevieve Garrant. The "Marie Genevieve" change to "Mary Jane" is pretty straightforward and common. Its also even easy to understand from a non-technical standpoint. But for reasons that I won't go into, the change from Garrant to Garrow is both less intuitive and more complicated. Suffice it to say that there are a LOT of variations of the name of that family as it lived in Quebec and migrated down into New York. In fact, I've got both Garrands and Garrows and Garrant's in my family tree and they all originate from the same ancestors.
I'm lucky enough to have connected with a guy in Indianapolis (originally from Mooers, New York) who has helped me in some research. Mostly out of the goodness of his heart but also because its research for him too -- we discovered we are 4th cousins 1x removed (he descends from one of Jane Garrow's siblings). He forwarded me this document and was kind enough to include a translation.
Last night, Jonathan wrote to me:
I found the baptism record (attached) of Jane Garrow (Marie Genevieve Garant in the record) from 1817, in the Drouin collection (attached). She was born March 18, 1817 in Chambly, Quebec, and baptized March 20, 1817 at St. Joseph's in Chambly. Translation of the record (maiden are used in Catholic records):
March 20, 1817, by the undersigned priest baptized Marie Geneviève, born the 18th of the same month, of the legitimate marriage of Joseph Garant, day laborer in this parish, and Geneviève Mâcé. The godfather was Pierre Mâcé and godmother Geneviève Lanier, who didn't sign, also the father was present.