If you type “Green Lantern” and select “name,” it will return John Stewart (II). That’s because it’s picking it up as an exact match from the nickname, which is part of the search criteria.
I’m guessing that if you don’t select what you’re looking for, it returns the only exact match it finds, which is the nickname for John Stewart (II).
Now. . . whether or not that is really his nickname is another question. Maybe, maybe not, since I don’t know the chap personally. However, it wouldn’t be totally unlikely, in much the same way that there might be people named “Hal Jordan” or “Alan Scott,” with the same nickname. (Not quite so likely with Guy Gardner, though.:D)