What Are The Terms For The Leader In Buddhism?

Do you mean other names for the Buddha?  Do you mean by what conditions (terms) can someone become a leader in Buddhism...?  Do you mean modern leaders of Buddhist groups?
I'll assume you want epithets (other names).  If that's wrong, let me know.

The Buddha was known as:

• "Bhagava", meaning "Sublime One" or "Exalted One"


• "The Arahant", meaning "Worthy One"


• "Samma-Sambuddho",  meaning "The Fully Self-Awakened One" (i.e., no teacher taught him how to become enlightened, he figure it out for himself)


• "Sugato", meaning "Blessed One"


• "Lokavidu", meaning the "Knower of the Worlds"


• "Supreme Trainer of Those Who Wish to be Tamed"


• "Teacher of Gods and Humans"


• "Buddho," meaning "Awakened One"


• "King of Peace" or "Prince of Peace"


• "Sakya-muni", meaning "Sage of the Sakyan Clan"  (his father was of the Sakya clan)


• "Recluse Gotama" (his mother was from the Gotama clan)


• "The Elephant Among Men" (or the lion, or the bull, or the "Leader of the Herd")


• "Enlightened One"


• (People who didn't like him sometimes referred to him as "That shaven-headed recluse.")

There are more, but these are all I can think of at the moment.   I hope this answers your question.