Thoughts in random order:
It's Japanese territory, they can call it Hidikie's Hot Rock for all it matters, it'll still be Iwo Jima to those who matter to me.
Japan has been one of our better allies in many ways since the end of WW2 but they do spend an awful lot of time and effort trying to pretend that WW2 never really happened.
Oh well, if they weren't foreign devily in their ways, they wouldn't be foreigners. Not having the strangeness of foreigners would take half the fun out of traveling.
So, rewrite the maps and apply your new labels but it's still our Iwo Jima.