Researchers with French ancestors are sometimes confused by the common usage of a "dit" name. An example of such a "dit" name is Joseph Paquin dit Pocha. Joseph is the first name, Paquin is the family surname, and Pocha is the dit name. A "dit" name is an alias or nickname attached to a surname. In contrast to a nickname given to an individual, a dit name is often given to distinguish between branches of a family. Its usage exists mostly in France, New France, Acadia and even the Métis population of Canada.
Some "dit" names seem to suggest the origins of the families, such as Orillon dit Champagne. Other "dit" names suggest an occupation or military connection. For example, the dit name "Tranchemontagne" as in Garceau dit Tranchemontagne means "mountain slicer," suggesting an ancestor who worked in a quarry. A given name could also be used such Hébert dit Manuel, where Manuel is the Christian name of the male head of the particular branch of the Hébert family.
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As a descendent of Jean Garceau dit Tranchemontagne, I of course asked what the translation of tranchemontagne was. I found that folks who learned French in school or not as their first language gave me the answer that you propose, Mountain Slice however in asking older generation French speakers (my grandfather one of them) the translation to them is “hillbilly”.