The word Opossum has the same structural problem many older English words had that started with a vowel, that they're cumbersome to use in speech with English's article system of "a" "an". Sometimes those older words naturally go through a shift where the N of the preceding AN is attached to the word ( an Ewt -> a Newt). And sometimes the leading vowel is dropped to favor the word starting with the consanant. 

Opossum sounds an awful lot like A Possum when speaking, so the animal gained Possum as a significant alternate pronunciation. The Australian possum, by they way was named after the north American one. I think in modern times, language is often pushed back into written form and policed by those intending to "be correct" in their English. So you see people correcting others who say Possum, by pointing out that only the Australian one is possum, the American one is Opossum. But both are correct, and in a different time, i bet the word-shift would happen fully and both animals would be Possum, regardless of their taxonomical or scientific names.