Then again, it at least sounds as if it used to mean Government rather than Cool Unique Corporation Brand originally. Back when Earth was just Earth, that is. (Or was it always one of those things that call themselves bigger than they are - say, like The United States National Presidential General Sewing Supplier Co. might be a single room in a Bronx basement run by two elderly ladies and having three regular clients, two of whom only ever come for the tea?)
I doubt there was much central control to ECS, of course - it just looked less anarchist if somebody was allowed to slap an official umbrella name onto that unholy gaggle of individualist profiteers. And we don't know if an ECS registry means a ship bows in the direction of ECS. Might be clever branding: "Earth Cargo Ship" would be the common Earth Cargo Authority prefix for all Earth cargo ship registries from whichever company, out of the hundreds out there, but a single company would choose to call itself "Earth Cargo Service" and adopt a cool logo saying so, so that it could usurp those three letters for commercial purposes.
That is, in the end, the big organization in actual episode dialogue is not ECS, it is ECA (that's the party that gives out the licenses in "Horizon", say). ECS is just the prefix for the name, and to the registry. And possibly the name of an individual corporation. But one may read canon in multiple ways.
And alas, it doesn't sound as if one is going to be contradicted by additional evidence from, say, DSC - as a dramatic element, ECS and ECA are probably dead both, as Earth herself in fact hasn't made a single appearance in DSC yet! It's all on the general level of the Federation now...
Then again, Boomers might still exist as a thing. After all, Sulu in "Friday's Child" is adamant that "a freighter's" speed as late as the 2260s still remains no higher than Warp Two... Not the speed of "the freighter", but the speed of all of them.
Timo Saloniemi