yeast, leaven, surname
麴 centers on fermentation starters made from grain: yeast and leaven used in brewing and baking. The surname meaning is a separate application of the same character.
麴 combines 麥 (wheat/grain) with 匊, which likely contributes the sound and relates to the idea of fermenting grain into yeast or leaven.
The left side 麥 shows grain, and the right side 匊 looks like something being wrapped and fermented. Picture grain being packed and left to ferment into yeast.
For キク, imagine a brewer adding yeast to a vat and saying 'kick' as the fermentation starts: kick -> キク, and the yeast kicks the brewing process into action.