Well, aside from the most common name swiss cheese plant, Mexican breadfruit is another "common" name for this plant.
Never heard it called any sort of 'breadfruit' and its fruit is nothing like a true breadfruit since it is an aroid and more closely related to things like the philodendrons and pothos.
The only other name I've heard Monstera deliciosa called –besides swiss cheese plant– is 'ceriman', but a search on Google turned up on the Purdue Hort. site that in Mexico and Central America it is often called 'piñanona' or 'piña anona', which I'd not heard used before.
OK – HTH
Paul M.
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Yes, I have no idea who came up with this ridiculous name...not an artocarpus species. Just google common names for monsteria deliciosa; there are a lot. Common names were probably made up due to culture, location, plant characteristics, or not knowing the real name of the plant.