Kahn decided on the name 'Misthios' as their soon-to-be-founded mercenary guild. As for why did he choose to form a new guild instead of joining already existing ones in Alfheim?
Being a Mercenary, the risk of their identities getting revealed would far be less and they could choose whatever type of job they want.
From finding herbs in forests like a beginner RPG game to killing an army of monsters… the Mercenary trade could do whatever their clients demanded.
Also, this trade had much more money and fewer restrictions than Adventurers Associations that kept tabs on you and had means to know your whereabouts in the name of offering protection and following the rules of the institution.
Just like the Mobile phones on the earth, the Adventurer Association's IDs were like tracking devices and chips that could be used to find you by law enforcement and authorities.