My name is Francis. How do I write my name as a possessive noun?
If it's singular, Francis's. If it's plural and your last name, Francises'.
Normally, an apostrophe and then an "s" is used to show ownership. For example, my name as a possessive noun is Parzival's.
When the noun ends in s, we put the apostrophe behind the s but don't add another one. So for Francis it's Francis' and not Francis's.
(Edit - I just found a big conversation on the subject. Apparently my answer is "old school" and the newer convention is to write Francis's. Whether you go old school or new school, this is apparently a matter of style and not necessarily grammar. Stay consistent and if you are writing for someone (whether it be for a class or an editor), just be sure to match your style to their expectations. Here is the conversation: http://absolutewrite.com/forums/archive/index.php/t-242529.html)