Reza Shah explicitly asked the international community to refer to the country as Iran and not Persia in 1935. I hardly think it's cultural bullying to insist that your identity is what you call it and not what someone else calls it. For instance, someone may refer to me as "Fuckface Shitstein". They're free to call me that if they like; but that's not my name. It's also significantly different than if someone calls me Sasha or Oleks in their language as opposed to Alex, which is what I call myself in my own language; they refer to me differently than I refer to myself but I understand that the distinction is due to linguistic difference. If I ask them to call me Alex instead of what they're used to calling me, it's reasonable for me to expect them to be polite about it and for me to take offense if they explicitly refuse to call me what I've asked them to call me for their own comfort.
Also, minor quibble but it's España, not Espagne.
My apology for the brain fade moment on Spain using French from habit.
I think the confusion may be due to a difference between identity and title. Of course an Iranian or someone from Myanmar have that as their identity, but to an Anglophone, Persian and Burmese are received English terms for the same things. I am well aware of the errors that induced the English terms but they became the traditional forms and using them simply refers to the same thing as Iran or Myanmar; however inaccurate their derivation e.g. the Burmese form only a part of the population of Myanmar. There is a difference between respecting that a nation and people call itself by a particular name and that of demanding that the world change it's everyday speech to match. It would be wrong of me to use a deliberately pejorative name for another country. That is gratuitous rudeness. But to use the existing traditional name in one's own language is a right of an independent people and culture.
I indeed find it irritating that foreigners use, even when using the language, English as a synonym for the United Kingdom which denies the separate existence of England as a nation within the Union but I do recognise that 'England' is a traditional synonym for the United Kingdom and when they use 'English' they are referring to the United Kingdom and not England; however mistaken. Except in sport where England proper has it's own identity. Persia is a traditional synonym for Iran. Burma is a traditional synonym for Myanmar. No diktat will change that fact. In Farsi I would use the name Iran. In Myanma bhasa (have I got that right?) I would use the name Myanmar. In everyday English I would feel free to use Persia (actually I would not as it is old fashioned) and Burma as freely as I use Poland and Morocco. When I speak to another of the original peoples of Morocco I use the term Berber because it is the received and understood term even though I prefer the 'Amazigh' of my remote ancestors. Amazigh does not carry over the Arabic cultural inferiority of Berber but nowadays, to non-Amazigh, 'Berber' just is a synonym of 'Amazigh'; whatever the nuances of it's origins.
Again simplifying. It is reasonable to ask others to call you by your preferred name. It is unreasonable to demand that they must only use that name amongst themselves. It is not my name but were I known as 'Dave' I can reasonably ask to be called 'David'. It would be unreasonable to berate others for calling me 'Dave' between themselves. Of course if they call me 'that ..**! Dave' that would be wrong and rude and I would have good reason to complain and be tempted to strike them smartly about the ears.
To address the OP. I am not aware (open to correction) that Persia was ever thus named by the good inhabitants of the country so they would have no need to rename it Iran as it was already Iran. If the government of Iran asked for the international community to use the Iranian name (i.e. Iran) it would do so but use Persia informally amongst themselves. The informal practice would reduce as time goes on.
There was, of course, the order by Churchill in WW2 that British forces and maps cease to use 'Iran' and instead use 'Persia' simply because of the obvious danger of confusion in English between Iran and Iraq due to their similar spelling and contiguity.
i think that we have exhausted the digression from the OP.