@InFinaLynx (or I guess whoever decided to use the whole Y'all thing)
just like the user before me mentioned, Y'all places the apostrophe before the "a". Additionally, if we are being completely true to "Southern US" english for this matter, the more proper way of stating that phrase would be "(All) Y'all's Names" as "all y'all" is typically used for larger groups with an indefinite maximum number, while y'all can be used for as few as 2 people, sometimes even used for a single person, but less so.