Is naming a newborn girl "Dan" permissible in Islamic law, knowing that the name is derived from Allah's saying: "And the fruits of the two gardens hanging low" [Qur'an 69:23], and it has other meanings that may be disliked?

There is no objection to naming a girl "Jana." Its meaning, as stated by the exegetes, is "the close fruit of Paradise." Among the best names for girls are the names of the Mothers of the Believers and the women of the righteous predecessors.