Is it permissible to name a girl "Fajr"?

There is no legal impediment to naming a girl Fajr. In the Arabic language, Fajr refers to the light of dawn and the redness of the sun. The criteria for prohibited names are those that involve servitude to other than Allah, or names exclusive to Him, the Exalted, or names that are ugly or involve self-praise. Other than these, there is no objection to using a name, with preference given to choosing beautiful names.