I mean you could... but good luck getting global agreement on that and realistically no. It is a thing that sounds nice and could look nice on paper but real world complications will result in issues pretty fast. Sounds like a great way to start a war as treaty violations will be inevitable and unavoidable.
If you divide up by altitude: it requires significant negotiation to place a vehicle (an arbitrary spacecraft or satellite) in any location.
If you partition by location (e.g. project current airspace upwards): your vehicles can't abide by these rules. They must orbit the planet. They will eventually go over most countries.
If you partition by orbit: you have to contend with precession. Craft drift[0,1]. This is because Earth is an oblate spheroid and not a sphere. It is also caused by angular momentum itself, so your orbit rotates. You will start in one and over time move into another. There's not much you can do about this and it is quite costly to maneuver (constant orbital maneuvering means an exponential increase in weight, complexity, and cost). Remember, the Earth does not rotate around in its axis in a fixed period of time, nor does it around the sun.
So really the laws of physics have you in a bind. Things are constantly moving and changing. So even the best laid plans will eventually lead to violation (and thus conflict) even through no ill-intent.
This is actually why a lot of (especially "hard") Sci-Fi has treated space travel as a global unification period. Because it becomes necessary in order to avoid conflict. This was a bigger discussion in the 60's and 70's when the initial space ventures were occurring and in the public eye, but has naturally drifted out of conversation as the underlying motivation similarly did. Though it stayed in conversation for domain experts who frequently content with this still.
tldr: No. Physics is a bitch
[0] https://en.wikipedia.org/wiki/Nodal_precession
[1] https://en.wikipedia.org/wiki/Apsidal_precession