According to article IV in Oxford's rules of apostrophes:
Because you pronounce the extra s after the name, Ziggs, it is actually correct to punctuate the possessive form of this said name to "Ziggs's". This exception in punctuation differs from other variations of names that end in an s such as the name, Thomas, as stated in the example, in which an apostrophe would come after the s in such a case.
Rules for such elision dated as far back as the 16th century, introduced by Geoffroy Tory, as an attempt to imitate the French language. However, standardization did not follow through until the 18th century, and was not universally accepted until the 19th century. Since then, however, this rule has existed and has not changed, and many fluent English speakers incorrectly punctuate the possessive form of cases like "Ziggs's" because it simply appears strange relative to what is normally seen.