If the name Iram Fatima is commonly used among people who speak your language and people from your country, and it does not carry any meaning this is contrary to Islam or its etiquette, then there is nothing wrong with using this name, because there is no condition stipulated in shareeah that the name should be mentioned in the Qur'aan or Sunnah, or that it should be an Arabic name, and there is nothing in shareeah to indicate that it is preferred for non-Arab nations to use Arabic names. Rather one should avoid using names that are exclusively used by followers of other religions and that are usually used by the followers of other religions, such as George, Peter, John, Matthew and so on. It is not permissible for the Muslims to use such names because that is imitating something that is exclusively theirs.
Quoted from Ahkaam Ahl al-Dhimmah by Ibn al-Qayyim, 3/251.
But if a non-Arabic name has a good meaning, there is nothing wrong with using it and giving it to one's child. The Messengers and Prophets (blessings and peace of Allah be upon them) had good names and gave good names to their children that were based on their customs and traditions, and they were not Arabic names. Such names include Isra'eel (Israel), Ishaaq (Isaac), Moosa (Moses) and Haroon (Aaron).
Imam al-Mawardi (may Allah have mercy on him) mentioned some matters that are mustahabb with regard to choosing names. Among other things he said:
(The name) should have a good meaning and be appropriate to the situation of the person to whom it is given; it should be a name that is usual among the people of his class, religion and standing. End quote.
Naseehat al-Mulook, p. 167
Because this word, Iram, is not used in Arabic we looked for it in other languages and - from looking on some websites - it became clear to us that the name Iram is used for females in some Muslim countries and its meaning in their language is: a garden in Paradise.
If that is in fact what it means in your language, then there is nothing wrong with using this name; in fact this is a good meaning, but we did not understand why it should be added to the name Fatima, because Faatimah was not singled out for Paradise to the exclusion of other women. So to be on the safe side it is better to choose just one of the two names, either Fatima or Iram, if that is customary in your country.
And Allah knows best.
Reproduced from Islam QA