What is the ruling on naming girls "Razan" and "Rawdan"? Does "Rawdan" mean a wise woman? And what is the correct vocalization of the word, with an open "ra" and "waw" or with a Damma on the "ra" and a lengthened "waw"?

There is no objection to being named Razan, for it comes from razanah (dignity, composure) and anaah (deliberation, patience), both of which are qualities beloved by Allah. As for "Rawdan," its meaning is going, coming, and revolving, and it might be the name of a place. There is no objection to being named with it, but other beautiful names are more preferable.