Being a "Hairston" - means their ancestors were enslaved on one of the MANY Hairston plantations. It also means that some - not all -- after Emancipation kept the Hairston surname.
Ok fair enough. Most black biographies that I have read are of the mullato offspring of the slave owning family. So they are related to the slave owning family both by blood and by name. Which is why I wouldn’t have characterized the Hodge twins as Hairston’s because although they were owned by the family, they are neither descended from a white Hairston and neither did they take the Hairston name. They are descended from a Hairston overseer and a slave by the name of Hodge. Which is different from the Hairston’s that I know who are descended from a white Hairston and have the name and if I were to ask if the Hodges are Hairston’s, they would most likely say no because they don’t connect into the same pedigree.
But based off of the definition you provided, “being owned by”, I guess you can loosely say they are Hairston’s.