What is the correct use of the apostrophe for a sign that reads Future Home Of ... Family's last name?
The use of apostrophes in last names is no different from their
use in any other word. If you are referring to a house to belong to
a family named "Smith," the sign would read "The Future Home of the
Smiths." No apostrophe: it is merely a plural noun. If the phrase
were "The Smiths' Home," that apostrophe is correct because you're
using the plural possessive: the house belongs to more than one
Smith. People who write things like "The Smith's" are incorrect (as
was the previous answer to this question). General Point If
you indicate possession by using of you musn't also use
's or s'.