Just as post-monarchical countries like Germany and Greece still have members of their former royal families who claim titles I'm sure Trek Era Britain also has Windsors who claim ties to a King or Queen from centuries before.
"My great-great-great-great-great-great-great-grandmother was Queen of the United Kingdom, you know! Elizabeth Windsor!"
"That's lovely, dear. Did you want another steak with your grocery order?"
"Sure, I've got enough Federation credits on my UBI this week I can afford to splurge."