Yes I know. I study Japanese after all.
It is not an official name though I mean from the Japanese Manga. It was created by 4kids dub and it is a direct hint to the Japanese Shadow Games which is called "Yami no Geemu" in the original.
The word is the English "game" with Japanese accent. The original word for game is "Yugi" (pronounced "yuugi") so the term "Yami Yugi" in reality means "Dark Game" aka "Shadow Game"