The French apparently were respectful of indigenous Cree customs, and named the lake "Grand lac des Esclaves" in translation.
'It has been suggested that the lake be renamed as well, particularly because of the mention of slavery. "Great Slave Lake is actually a very terrible name, unless you're a proponent of slavery," says Dëneze Nakehk'o, a Northwest Territories educator and founding member of First Nations organization Dene Nahjo.' He seems to be Athabaskan himself, and of course would prefer a native Dene name. But he calls himself cis-Indigenous, so I'm not sure how representative he is of the Dene.
Indigenous customs seem to conflict here: Cree vs Dene. The Canadians could draw on the liberal Western tradition and put their finger on the scales in favor of changing the name. Of course, that would be a form of cultural imperialism.
Think what other options there are: Leave the name alone because changing the maps is expensive, let Cree and Dene each pick a name and use both, let Cree and Dene pick a name and pick wrestlers to fight it out, go a different direction and name it St. Kateri Lake, name it Lake George Floyd, sell naming rights (and end up with Toyota Lake?)--on and on. You could find support and/or tradition for all of those.>