Good question! I guess you mean that she would always be called by both names?
Let’s see. These are the ones I like:
Mary-Ann and Mary-Anne
Mary-Rose
Mary-Jane (wouldn’t use, though)
Lily-Rose (but might be too celebrity associated)
Ruby-Rose (I know there is a celebrity named this and it might be too much)
Chloe-Rose
Eva-Marie
Eva-Maria
I would choose Lily-Rose because [name_f]Lily[/name_f] is my favorite.