Board Thread:Questions and Answers/@comment-26527791-20150704145537/@comment-5916303-20150704161120

In the first episode of Amnesia's custom story: Late Night Drink, Mark made a joke about calling a small box "Tiny Box Tim" (he stated that he finds small things, like plushies, to be adorable). It sort of caught on with the fans and eventually, he transpired into a mascot.

As for Warfstache, I haven't been long enough to know the story behind him. Hopefully someone else will clue you in.