Should a last name have an apostrophe for possessive?

Yes, a last name should have an apostrophe for possessive use. For example, if you want to indicate something belonging to someone with the last name Smith, you would write "Smith's." The apostrophe and the letter "s" show that the item belongs to the person named Smith. If the last name is pluralized, such as "the Smiths," you would use an apostrophe after the "s" (e.g., "the Smiths' house").