GM KIM Soo Jin from Atlanta, Georgia, who is one of the most senior Jidokwan members or the senior Jidokwan member in the US, says the school name was Kwon Bup Bu. So did GM LEE Chong Woo in at least one interview:
“It was right after the Liberation. I suppose it was a dream of my adolescence around the age of seventeen, and I had the vague hope of becoming an unbeatable martial artist. When I heard there was a particular place in So-Gong-Dong, Seoul where they could train someone in the 18th method [known as a
Chinese form of martial arts] I went there. It was a Judo school during the Japanese occupation period, and they used to put out a sign saying, ‘Chosun Yeon Mu Kwan’ in which they had a Judo Division and Kwon Bup Division. From then on, I learned Karate in the Kwon Bup Division. Kwon Bup is the same as Japanese Karate. Since the national pride was concerned, we called it Kwon Bup instead of calling it Japanese Karate.” -- GM LEE Chong Woo
“In the beginning, Judo was the major martial art course at Chosun Yeon Mu Kwan with a small section of Kwon Bup in it. However, the Chosun Yeon Mu Kwan was put into service during the Korean War. Byung Suk Lee, the President of Chosun Yeon Mu Kwan was a nationalist. So, people in the Kwon Bup Division moved out of the center to another location due to the delicate political circumstances. The Korea Gymnasium, which was located at Ulgiro 3rd Street, was then
the site of the Ji Do Kwan.”
“It took me over a year to become a first degree black belt, then 2nd degree black belt and 3rd degree black belt, and then the Korean War broke out. By the time Seoul was liberated, I was going to test for 4th degree black belt, but I had to have appendix surgery. So, I received my 4th degree black belt through a
recommendation while others took the performance test. After the Association was established, I received a 9th degree black belt. At the beginning, I received the 1st degree black belt in Kwon Bup and then I became a 9th degree black belt in Taekwondo. The name changed.”
I asked GM LEE Chong Woo directly in his office at the Kukkiwon way back when, and he told me the name was "Chosun Yun Moo Kwan Taekwondo Bu". He even wrote it out for me on a piece of paper which I still have.