The word 'Ogi' has its origin in 'afugi (あふぎ)' (something which creates wind) which had derived from 'afugu (あふぐ)', and it has been hard to ascertain the association between the words.
「おうぎ」は、語源は「あふぐ」（扇ぐ）の派生形の「あふぎ」であるが、日本語の変化により関聨がわかりにくくなった。