I have tried everything including re-seting my UI, but the names, not the nameplates will not stay turned off. When I reload the setting are set back to the default.
I had a similar issue and found the answer here : Interface->Names->NPC Names reset & won't save changes - #6 by Merilwen-hyjal
Tl;dr : If you’re using ElvUI you need to disable it under their new options.
ElvUI > Name Plates > General Options > Name Visability.