For you it seems they'll be flying Space Patrol Vehicles around, using their Blues-And-Twos to pull over any errant rockets. "Good morning, sir. I don't suppose you know the reason I asked you to pull your rocket over to the edge of the orbit. Were you aware that the speed limit is strictly 7,000 mph on the geosynchronous ringroad?"
https://youtube.com/watch?v=O8YiXdTP-5EOr maybe maintain a set of ground/air-launched soft interception grab-and-deorbit missiles ready for
OOSS/
MEV-style take-overs of anything that gets launched outwith acceptable parameters. The problems of which have been discussed ad nauseum.
I think it'd be more an administrative/legal body, coordinating future intentions and retroactive resolutions with the promise of convenient and hassle-free exchange of information (with sufficient corporate/strategic confidentiality) as the carrot and the threat of potentially heavy internationally-enforcable fines (for private concerns) or binding resolutions (against states) as stick to try to ensure compliance to whatever principles need to be be agreed through goodwill and mutually acknowledged necessities.
(While a force may need lawyers, commissioners and administrators, I can't see a bunch of lawyers, commissioners and administrators themselves being called a 'force'/wear insignia, with those they have to liaise with keeping a straight face.)
Hmm, a Commission? Have it be an Earth Orbit Cordination Commission (perhaps extending through to lunar/lagrange 'territories' at least this side of any trans-solar cessasionist movements), with some Space Traffic Control as the real-time multinational monitoring and reporting service.