The origin of this nickname was a misunderstanding. When the crew of the USS Voyager met Neelix in 2371, Captain Kathryn Janeway introduced herself as "Captain Kathryn Janeway of the Federation starship Voyager".
Neelix must have thought that the Federation was Janeway's species, as he later said to Tuvok: "You Federations are obviously an advanced culture" when he was beamed aboard. Tuvok tried to correct the misinterpretation and told Neelix "The Federation is made up of many cultures. I am Vulcan". Neelix misunderstood again, and now assumed that 'Vulcan' was Tuvok's name, and hence started to call him "Mister Vulcan". (VOY: "Caretaker")