@Ovnidemon I am not sure myself and would like a reminder from the translators, but I guess it goes:
1) Martial Arts League = Murim Alliance, the same guys who were trying to lure people into rescuing the kid and then take the kid from the protag, some guy is reporting to his boss of their failure.
2) Soo-Gi = Mak-Soo (formerly Maksoo), the protag's estranged friend with water powers, one of the so-called Ten Demons.
3) Noble Yuk = the high-level master guy with swords and gray hair from the Martial Arts League who was chasing the protag and got a mutual knockout with him in this chapter.
4) Sal Moo-Bang = some really strong guy in one of the organisations???
5) Noble Neh = Noble Yuk???
6) Noble Hee = another pursuer, hasn't appeared yet.
7) Rampaging Blade and Heavenly Dragon = might refer to the organisations for one of which the protag works (Sword Clan and protag's workplace, the Heavenly Dragon Association).
Aside from Yuk and MC's friend all these are pretty much my guesses.