Actually, I think most of us who use the Japanese name have taken to calling the original movie Gojira to differentiate it from the Burr version.
Othwise, rather than writing one word, we end up writing, "Godzilla, but not the version with Raymond Burr, the original Japanese version," or "Godzilla, but not Gozilla King of the Monsters"--as if most people would even understand the difference.
And, since there's now a US version of the original called Gojira, it just seems simpler to use that name.
For me, anyway.
It is odd, though, when you get different version of movies for the US and foreign audiences. The uncut, Chinese version of Once Upon a Time in China it great -- the Americanized version only so-so. I guess we could call the original by its Chinese name, but I'm sure it's more than one word and hard to remember.
Hoping other folks will weigh in on 50s sci-fi -- SDS