Analysis of information sources in references of the Wikipedia article "쌍둥이자리 델타" in Korean language version.
Wasat and Wesat are from Al Wasat, the Middle, i.e. of the constellation; but some have referred this to the position of the star very near to the ecliptic, the central circle.
The name is a mess, "Wasat" meaning "middle" in Arabic, but the middle of WHAT is not clear, whether the middle of Gemini, of the sky, or of the neighboring constellation Orion (which the Arabs referred to as the "Central One"), the star name improperly applied to our Delta.