But in the article below, it uses possessive noun (Michael's family). Does it mean that possessive noun is allowed when using the first name but not the last name?
If by re-arranging the word order you can put an "of" in to replace the apostrophe then you should use the possessive. So another way of saying it is This is a gift from the family of Jordan, though in this one you would probably put in the Firstname too.
The only time you don't put in an apostrophe is when you use pronouns. So his, hers and its DO NOT have apostrophes.