What name can we use for Go in Latin?
Here are some ideas.
1. From Japanese 囲碁 (igo). The Japanese word has a short 'i', so we should make the Latin 'i' short as well. Result: igō, gen. -ōnis. 'igo' is the name used on Wikipedia. We could also use Old Japanese wigo. Result: vigō, gen. -ōnis.
2. From Mandarin 圍棋/围棋 (wéiqí, wei-ch'i). 'v' translates 'w'. 'ē' translates 'éi'. 's' translates the 'ch'-ish sound of 'q' (see chocolate => socolata). '-is' translates '-i', since we want our term singular. Result: vēsis, gen. -is or -idis.
3. From Korean 바둑 (RR baduk, MCR paduk). The 'a' is short. Although the 'u' is also short in Korean, I think it should be long here in Latin, like in cadūcus (drooping). It would be vulgar to leave 'k' before 'u', when in Latin it should only precede 'a'. Whether to use 'b' or 'p' is a matter of taste. Without a lead from the word form, we can't do better than to use the ending and declension of lūdus, game. Result: badūcus, padūcus, gen. -ī.
4. circumveniendi lūdus / lūdus circumveniendi, 'the surrounding game', as used in De Ludis Orientalibus Libri Duo.
5. From English et. al. Go. Result: Gō, gen. Gōnis; or gō, gen. gōnis. It's not too short, since both dō (give) and nō (swim) are common words. Wikipedia has 'Go' as the name in almost every language with the Roman alphabet.
Esperanto Goö is, as well as ugly, probably not even permitted in Latin phonology. But Gōsō or Gosō seems reasonable.
Dieter: a literal translation would be "ludus circuitum". An idea I like is "ambitio" because ambire in Latin means "to surround" and for its obvious modern connotation.
bugcat: I found some pronunciations from other Chinese languages. For comparison, we started with Mandarin weiqi => Latin vēsis.
In ancient Chinese it was called yi, which gives Latin jis or jīs. Or, if we want the word to be longer, jisis or jīsis.