Must the name of the two-year-old girl "Iman" be changed, and does the prohibition of naming with such names imply impermissibility?

The Lawgiver (Allah) encouraged naming children with good names and forbade ugly or disliked names. The Prophet, peace and blessings be upon him, prohibited names that imply self-praise, such as "Barrah."

Contemporary scholars differ on whether the name "Iman" (faith) implies self-praise or not: - Some believe it does imply self-praise, such as Sheikh Ibn Uthaymeen and Sheikh Abdul Rahman Al-Barrak, and thus they prohibit naming with it. - Others believe it does not imply self-praise, such as the Permanent Committee for Scholarly Research and Ifta and Sheikh Ibn Baz.

It is safer not to name with "Iman" initially, to avoid the اختلاف (disagreement). However, if the name has already been given and it is not easy to change it, there is no harm in keeping it.