My name is Habiba which means "darling" in Arabic. I am engaged to be married soon and my fiancé does not like my name due to the thought of other people (Especially males) calling me by my original name. Do you think that I am doing the right thing by agreeing with my fiancé to change my name?2. Is it Haram to communicate with my fiancé through emails and calls in order to get to know one another?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Changing names fits into two categories:
First, there can be something in the name that makes it Islamically dislikable; in this case it is likable to change the name. Some names are ugly so it is likable to change them to nicer names as the Prophet did to A'siyah Bint Omar Ibn Al Khattab. The Prophet changed her name A'siyah (which means "the sinful") to "Jamilah" which means "the beautiful". Some names contain arrogance and pride like "Barrah" (piety). The Prophet changed "Barrah" to "Juwairiya" (a little lovely girl).
Second, the name might not contain anything that is repulsive or arrogant. But the person wants to change it for some reason. It is lawful to do so. So, there is no harm in changing your name from "Habiba" to another name. The Hanbali scholars allow having more than one name.
We remind you however that the man you are engaged to is like any other alien man, as long as the marriage act has not been established. So, beware of having illicit relations with any man. Allah Says (interpretation of meaning): {… then be not soft in speech, lest he in whose heart is a disease (of hypocrisy, or evil desire for adultery, etc.) should be moved with desire, but speak in an honourable manner. }[33:32].
For more details, please read Fatwa: 81184 and 81668.
Allah knows best.