Is Branches correct plural proper family name?

No, "Branches" is not the correct plural form of a family name. In English, the plural form of a family name is created by adding an "s" or "es" to the end of the name, depending on the specific spelling. For example, if the family name is "Smith," the plural form would be "Smiths." It is important to follow the rules of grammar when pluralizing family names.