I don't think its embarrassing - especially not if she has a legitimate right to use the name. I mean if you had connections or something that would give you an advantage - wouldn't you use it?
It would be embarrassing if she was no relation of Hemingway's at all and pretended to be (like some actress went around pretending to be related to Edie Sedgwick awhile ago), but this is not the case, so i don't see the problem.
Besides, from what I know of Hemingway - he was quite the man-about-town himself, he wrote about the faded glory of america and the troubles of the working class, but i believe he himself attended as many glam cocktail parties as the best of them.