var name = "Jesus"
var message = string.Format("It is {0} birthday!", name.Possessivize());
// message == "It is Jesus' Birthday"

var name = "David"
var message = string.Format("It is {0} birthday!", name.Possessivize());
// message == "It is David's Birthday"

Of course, I know different style guides treat possessive forms differently, so this would need to have a configuration option.

For instance:
Some style guides the possessive form of Illinois should be Illinois' because it ends with an s, some say it should be Illinois's because all possessive nouns get the 's treatment, some say it should be Illinois's because the "s" is silent, thus the "s" in the `'s' would be pronounced.

I imaging it can get even stranger if you want a possessive plural (proper) noun that ends with an s, like Jones, e.g., "Let's go to the Joneses' house".

Note: I can't think of a word denotes the opposite of being possessive.