This was taken from the Merriam-Webster Guide in the section on "Plural and Possessive Names"
For names that end in an s or z sound, you can either add -'s or just an apostrophe. Going with -'s is the more common choice:
the car that belongs to Jones → Jones's car or Jones' car
But there are a few exceptions. For classical and biblical names with two or more syllables ending in s or es, you usually just add an apostrophe. If the name is only one syllable, add -'s.
Socrates' students
Ramses' kingdom
Amos' prophecy
Zeus's warnings
The names Jesus and Moses are always made possessive with the apostrophe alone:
Jesus' disciples
Moses' law
Based on this, you can either say Hogwarts' or Hogwarts's (pronounced HOG-warts-IZ). Both are correct.