The Guardian states the island was "always known" as Iwo To before 1944. The article goes on to say "It only became known as Iwo Jima because Japanese officers who arrived to fortify the island after its residents were evacuated got the name wrong." Research has shown this not true. The Eleventh Edition Encyclopedia Britannica (1910-1911) calls the island "Iwo Jima" in the "Volcano Islands" entry. The 1943 National Geographic Map of the World also identifies the island. As do earlier National Geographic maps.
So the Guardian is wrong. Catholicgauze cannot be for certain but it appears that "To" might be a regional name while "Jima" could be a mainstream/Tokyo word. What we have here seems to be a battle between locals and a dominating national culture. It is surprising to see local culture win in such a conforming country as Japan.
Final note: Do not expect to see information on the Battle of Iwo To; however. Conflicts in places that have changed names such as Leningrad/Saint Petersburg and Stalingrad/Volgograd use the historical name. So rest assured you can still rent movies with names like Letters from Iwo Jima.