Depends on the distance being traveled by both ships. The Milky Way is 1000 light years deep, so there’s a lot of vertical room to maneuver. Mentioned locations at real star systems, like Wolf 359, are definitely not all on the same plane in any way. Possibly more relevant, though, is that ‘up’ isn’t really much of a thing. Star systems can (and do) have their axis tilted significantly off of the galactic axis, so even if you define ‘up’ within a star system and orient your ship that way, you may wind up tilted weird when you arrive at the next system due to it having a different ‘up’. You could define ‘up’ by the galactic axis, but that would still only apply to the one organization; there’s no reason for the UFP, Romulans, Klingons, Cardassians, and Dominion to all agree that one side of the galaxy is the top and the other is the bottom, but they do anyway. Humans couldn’t even agree on which way to orient maps of our own planet for centuries.