The first advertisement for the game was in 1990, in a page where Nintendo Entertainment System Toho games were being advertised. The ad showed Godzilla: Monster of Monsters, Circus Caper, the Gameboy Godzilla, Times of Lore, and Rodan. Interestingly, the Rodan part of the ad states that Rodan is "Godzilla's arch enemy", however, the only fight they had fought up to the time of this game's production was in Ghidorah, the Three-Headed Monster, and that was only brief. Afterwards, they were shown to be allies.
Issue 16 of Nintendo Power mentioned the game in their "Game and Watch" section. This issue mentioned that the game is "sort of a sequel to the NES Godzilla game." In their September issue of 1990, Gamepro mentioned the game as well by saying that it was "a sequel to Godzilla."
Not long after, the game was scrapped and then according to Nintendo Power returned as Godzilla 2: War of the Monsters. How much of the game was changed when the game was renamed is not known. It's reported that the reason for the game being renamed was that Toho felt a game under Rodan's name wouldn't sell as well as a Godzilla game.