In "Histoire Genealogique des Familles de DuPuy-Montbrun et de Murinais", by Guy Allard, published 1681 (See https://gallica.bnf.fr/ark:/12148/bpt6k374329d/f18.item for a PDF of this book in the French National Library), the author says, speaking of Hugues' wife and the mother of Rodolph and Romain Du Puy: "I don't know the name of their mother, but it's pretty certain that she was the sister of Eurard de Poisieu, and that she had crossed the sea with her husband." (Hughes, his wife, and three of his four sons fought in the First Crusade.)
That sentence, in the original French, is "Je ne sais pas le nom de leur mère, il est pourtant certain qu'elle etait soeur d'Eurard de Poisieu, et qu'elle avait passé la mer avec son mari."
The words "soeur d'Eurard de Poisieu" jump out of that sentence. They are not a woman's name. Again, they translate to "SISTER OF Eurard de Poisieu".
If Allard's book is the source of this record, then Allard said plainly, "I don't know her name." And her name is clearly not Deurard.