I went to school with a girl called "Amy Smith".
Her mother was a fairly well-known scholar, who went by "Jane Jones". Jones was the surname of her first husband, who she had married early, before she got known. When Mr and Mrs Jones got divorced, Jane kept the name, because it was easier than hyphenating or confusing people with a name change.
A few years later, she married a Mr Smith (Amy's dad). As far as the law, their friends, and eventually the school (etc.) were concerned, she was Jane Smith, but she still published her articles and attended conferences under Jane Jones.
I don't remember anyone having any issues with it. It's the same as having a stage name or psuedonym, I suppose.