This really all stems from a misunderstanding of what "full stop" or "all stop" (all engines, for vessels that commonly operate only some engines for cruising) means. "full stop" is a position on the engine telegraph that tells engineering to stop the engine or take it out of gear, depending on the type of propulsion setup. It has nothing to do with the speed of the ship relative to anything, after the "full stop" order is given the ship will continue to move forwards by momentum. If the captain actually wants to stop as soon as possible they will order "full astern," which signals engineering to run the engine in reverse at normal full speed, effectively braking. Because oceangoing ships stop on their own reasonably quickly this is usually more of an emergency maneuver.
The fact that motion is relative is already quite true at sea in our own world, where in at-sea operations your position relative to other vessels can matter much more than your position relative to the earth. In other words this issue is not at all new or specific to space. More basically, though, today and presumably centuries into the future "full stop" is not an order to stop the ship, it's an order to stop the engine.
The order is "full stop" because large marine engines are traditionally directly coupled to the propshaft and cannot "idle" per se. On these types of systems, still common on large vessels, there is some nuance depending on the engine setup between "standby," "stop," and "finished" which are traditionally all positions on the engine telegraph that do more or less the same thing but give different instructions to the engineer operating the engine as far as preparations for the near future. On top of this most ships today the "engine telegraph" is not really used when underway and the telegraph sender on the bridge actually controls the engine directly via automation, but usually this only allows for speed changes and not stopping or reversing, which still requires that engineering take over engine control due to the preparations and checks that must be done when stopping and starting the engine. Rather than telegraph bells this is more likely to be a phone call these days.