I am unaware of an expression "pull and bear" in American English, so I would guess that it is an invention of the brand. Perhaps others italki members will have better insights. Pull and Bear is a casual, laid-back brand. So, perhaps it is short for "pull over" (as in putting on a casual shirt) and "grin and bear it" (enduring something unpleasant with humor).

I have absolutely no insights whatsoever. Never heard of the brand. What is it?