Do you know how to use multiple recruiters in Korea? If so, please share your insights!

Hello! It's been a year since I came to Korea, and I'm currently preparing to work as an English teacher in Itaewon. My friends have told me that it's good to use various recruiters. However, I'm confused about what to do if a company asks me who introduced me. Should I just cut off contact with other recruiters? I have applied to Korvia and plan to apply to Korean Horizons as well. Can anyone recommend other good recruiters? Any advice would be appreciated!