I'm not sure that I understand the question. Are you just looking for an example? If so, Mary-Ann (or Mary-Anne) is quite a common one.
Yes, you understood the question.
In Michel Tournier's French novel "Les Météores", there are two twin brothers, Jean and Paul, whose mother calls them as if they were one person: Jean-Paul. One of the twins is going to die, and his brother will bear his brother's name by the compound first name.
If you have a slightly less common example.