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Powys/Powis is a Welsh place name. My first ancestor of that name was Hawys Gadarn "the Hardy", daughter of Owen ap Gruffyd, Prince of Powys-Wenwynwyn & Johanna Corbet, born 1291. She married John Cherleton, 1st Baron Cherleton de Powys. This line daughtered out for me with the 1421 marriage of Joyce de Cherleton in 1421.
Surnames came into existence after the Battle of Hastings in 1066, when William the Conqueror decided to take Inventory of his new holdings. This inventory was called the Doomsday Record and necessitated the use of surnames as identifiers. Before taxation, there was no particular need for surnames. Some German families of ancient descent still don't use surnames. Their titles are their surnames.Of course, they didn't have to answer to Wm the Conqueror.
Surnames were usually descriptive, i.e. "of" a certain place, hence the term place names. Place names often imply a Norman origin, since they were the ones who usually owned the land and had place names associated with their estates/lands. Others were occupational , or patronymic, like Johnson for John's son.
That about covers my limited knowledge of the subject.