The Japanese name is actually 囲碁 (igo). 碁 (go) is just an abbreviation; I don't see it often in Japanese text, but for some reason the Anglosphere decided to adopt it.

囲 is a simplification of 圍, and 碁 is a Japanese-specific letter that roughly maps to 棋. If you read 圍棋 in Chinese, you get weiqi.