There have been many discussions about dit names on the net, and not only for Deslauriers.
Dit names may be attached to the original surname for many reasons and are often adopted by the families to distinguish family groups in areas where the original name is widespread, or to conform to usage by their friends, neighbours and even officials. These dit names are attributed as nicknames related to geographic features, place of origin, trade, traits of character or borrowed from a female parent (mother or grand-mother in many cases, even the father's or grand-father's first name). Most Soldiers had the custom to take a "war name" or had one assigned by their companions or officiers, sometimes not very glorious names.
Here with Deslauriers there is only one family who's original name is Deslauriers to my knowledge (some descendents adopted Lafrance). Another individual by name of Deslauriers dit Lafranchise had no descendents. Other Deslauriers are originally another name that was changed to Deslauriers after a certain period of use in conjonction (dit is equivalent of SAID) with the original name, such as Renaud, then Renaud dit Deslauriers, then Deslauriers dit Renaud and finally Deslauriers (some even went back to Renaud after 1 or 2 generations).
Here is a non-exhaustive list of original non-related surnames that changed to Deslauriers. Note that some original surnames changed to several dit names.
Babineau, Basset, Bénard, Bonin, Bourseau, Cantara, Cavelier, Cordeau, Cordier, Cotineau, Dauplaise, Dion, Duchiron, Dufournel, Faureau, Favreau, Hébert, Jacquet, Legault, Ménard, Moreau, Normandeau, Renard, Renaud, Robert, Seleurier, Tinon, Vinet.