The 84Goji's name comes from the year the film it was featured in, The Return of Godzilla, came out (1984, because in Japan the film was just called Godzilla with no additional words to that title and Godzilla faced no monsters in it), and Goji, which comes from Godzilla's Japanese name, Gojira (ゴジラ?).
Due to problems with the mechanisms in the suit's eyes, his eyes sometimes face away from each other, giving a somewhat comical appearance which wasn't intended by Toho. This is particularly apparent during close-ups of the suit.
This suit was stolen from Toho a little while after The Return of Godzilla, and still, nobody has been able to find the suit, or the culprit, though it is highly unlikely that the suit is currently intact, considering how long Godzilla suits normally last.