Islam emphasizes that Muslims should have good names and give good names to their children. The Prophet (peace and blessings be upon him) is reported to have said, “You will be called on the Day of Resurrection by your names and the names of your fathers, so have good names.” (Reported by Abu Dawud).
Islam does not oblige Muslim people to choose specific names, Arabic or non-Arabic, for their children, whether boys or girls. It is rather up to people to choose the names for their children. However, the name should bear a good meaning and does not contradict the Islamic guidance in choosing names.
It is allowed to name your child Iman which means faith. There is nothing objectionable from the Shari`ah point of view to name your child Iman.