as far as performance goes it makes on difference which way up it is. and you can mount it how you like unless it fouls the frame during compression. does it have a piggyback? if you do swap it round, makes sure there's adequate clearance by removing spring (air charge if it's an air shock) and cycling the swing arm through the full arc of travel. – remember the bottom out bumper can be squashed almost flat on harsh bottoming. (if it's looking close, sit on the bike with no spring to make sure)
oh, rather than positioning it a way that you think looks best, position it so any adjusters are easy to reach, and out of mud spray if that's possible too.