The name Taekwondo didn't exist prior to General Choi naming it, but it was united by the Kwan leaders, not Choi. In fact, at the time, Choi only had "honorary 4th dan rank" not full regular dan rank, and that was (controversially) revoked by GM Son, Duk-sung in the Seoul newspaper on June 15th 1959 after Choi asked for higher honorary dan rank, so whether he was a legit master is even really in question.
Choi did a lot for popularizing and promoting Taekwondo, and for that I'm grateful, but let's not take credit from a bunch of honourable grandmasters who unified Taekwondo and give it to one guy, who in reality is the cause of the major split in Taekwondo. 9 Kwans (we'll ignore the 10th administration only Kwan) came together to unify to form Taekwondo, KTA, and then Kukkiwon. General Choi was the only one to split away - even his original Kwan Ohdokwan still exists in Korea and fully supports Kukkiwon.
Let's examine history a little.
First GM Son was no longer CDK president when he placed an ad in a newspaper expelling General Choi and revoking his rank. The same ad also expelled GM Uhm and GM Nam. So, questions should be asked if someone who was no longer president of an organization or even a member had the right to expel people and revoke their rank. We know GM Uhm was president after GM Son was gone and remained so for many decades. GM Nam remained a member as well. So, what does that tell you about GM Sons advertisement and efficacy of the purported actions contained therein.
Next let us look at what General Choi did. As head of the 29th infantry division, (using the name Oh Do Kwan being art of the genius) recruited, and trained top MA talent in a new system he developed so it could be taught on a wide schedule. Took trained people on world tours to demonstrate, dispatched instructors throughout the world to teach, recruited Korean instructors in other parts of the world (Jhoon Rhee a notable example) to start teaching the system . Lobbied endlessly against resistance to use the name.
There is no doubt he was successful do to his position and ability to access government resources.
I asked GM Nam, knowing how people were typically loyal to their instructors / Kwans how it was that General Choi was so successful (again the Name Oh Do Kwan comes to mind) that General Choi was so successful attracting people. His answer was because General Choi had access to resources no one else had. If they wanted to do a demo somewhere they would get on a military transport and go.
So there is no doubt the motivation was to spread a system on a wide basis taking a page from Funakoshi, Kano etc. with the advantage of modern travel and communications (along with the spread a public relations feat for SK)
Also no doubt the General Choi's success was due to political influence and resources.
Now, fast forward 18 years or so, the SK government uses it's resources to come up with TKD v2, and uses it's influence and resources develop a system, recruit, and train instructors, and dispatch instructors across the globe with the now even greater advantage of better communication and travel.
What other honorable GM came even close to duplicating General Choi's efforts / results notwithstanding his access to resources?