When writing any type of formal paper or even a document for your own use, there are certain rules regarding when you should and should not use an apostrophe. In regards to a person's last name, an apostrophe adds possessiveness to what you're writing. By following a few simple rules you can make sure you don't misuse the mighty apostrophe and end up looking silly.
Insert your apostrophe at the end of the last name. If you are adding possession and the last name in question is something like "Stephens" -- that already ends with the letter "S" -- write the last name as Stephens'.
Add an apostrophe at the end of the last name, followed by the letter "s," if the last name ends in any other letter. If the last name in question is "Thompson" add the possessive by writing it as "Thompson's."
Leave off the apostrophe for the last name, if you are simply pluralizing the name in question. If you are writing about a family with the last name George -- refer to them as the "Georges" instead of the "George's."