A living history group like the Society for Creative Anachronism is part sport, part research, and part improvisational theater. The theatrical part is called developing a "persona." My persona, the character I portray, is named Charles (the) Fleming.
When you flip through a book of historical costumes and pick one you like, you have also picked a particular time and place. Every fashion came from somewhere, after all. Whether you are shopping for accessories ("Does this kind of pouch go with my tunic?"), or branching out into a new activity ("What kind of wine should I brew?"), you find yourself learning more and more about that particular time and place.
What did they eat? Where did they live? Who were their enemies? How did they worship?
Not being historians for history's sake, most SCA members organize what they learn by creating a fictional character from that historical setting. Then, the things that they learn and make and buy become props for playing the character better. For some, it may be nothing more elaborate than taking an historic-sounding stage name. Others may strive to stay "in character" for a whole weekend, living and speaking as much as possible the way people used to do.
In my case, I wanted a "prime time" medieval experience. So, I picked the biggest city in Europe at the peak of the High Middle Ages. The city was Ghent, in what is now Belgium. My own un-used first name, Charles, was much more popular at the time than outlandish names like Wolfstam, so I was Charles from Ghent.
Family names as we use them today were practically unknown. Most people had only a given name and a "byname" that described their home town, father, or occupation. In the 1300s, Ghent was the capital of Flanders and, to an English speaker, people from Flanders were "Flemings." People from Ghent, believe it or not, were called "Gaunt." So, between Charles the Gaunt and Charles the Fleming, I chose the latter. I have some modern-day friends named Fleming, and they are quite amused to have me "in the family!"