I think traditionally younger players are taught to use their dominant hand on top, but I think it's one of those things you get used to depending on how you start playing (ie, my left handed friend plays a right handed guitar since his dad didn't know the difference when he bought him his first one).
In most of my beer leagues, there are way more RH shots since most of us in California didn't grow up playing so most folks assumed being right handed meant you were supposed to shoot with a righty stick. In particular, of the 30+ women in my co-ed ball hockey league, all of them shoot RH (and most of them picked up hockey as a rec sport as adults).
Although I think a few of them played field hockey and "lefty" sticks aren't allowed, so it made sense for them. On an unrelated note, the Olympic field hockey training center used to be in San Diego and we had a couple women who played in our ball hockey league. Their hand-eye coordination was insane, definitely gave me greater appreciation for Olympic skill level.