Researching an American female ancestor is relatively simple: she uses the name given at birth until marriage and until recently, took her husband’s name after. If she married more than once, she simply adopted the name of the latest husband.
It’s not that simple with a Luxembourg ancestor. Different rules apply in the U.S. and in Luxembourg. In Luxembourg, a woman uses her maiden name, although her children will use her husband’s name. Once she comes to the U.S., she follows the American model.
So in U.S. records, use married names – and in Luxembourg, use maiden.