I can't get a screenshot, but from turning on closed captions on Netflix, it calls him "Slurms McKenzie".
Go with that.
Got the same results when I enabled closed captions for the following clip on Comedy Central's website...
Since both Futurama wikis refer him as MacKenzie and as he "may be inspired by Spuds MacKenzie, the dog mascot of Bud Light beer", I'd say that's correct.
I saw that too.
Wiki's "Fry and the Slurm Factory" plot description refers to Slurms last name as "Mckenzie", as does IMDB.http://en.wikipedia.org/wiki/Fry_and_the_Slurm_Factoryhttp://www.imdb.com/title/tt0584439/fullcredits?ref_=tt_cl_sm#cast
Also, when typing "Slurms MacKenzie" into Google, it even pulls up the search correction "Did you mean: Slurms McKenzie?".
But according to Futurama Wikia and The Infosphere, both have the character's last name as spelled "MacKenzie"http://futurama.wikia.com/wiki/Slurms_MacKenziehttp://theinfosphere.org/Slurms_MacKenzie
So I'm still a bit conflicted as to which one is correct. But i'm inclined to go with "McKenzie".