I was tempted to write yesterday but I controlled myself. Today is another story. I find Greek names very interesting and challenging.
Zizos is a very unusual name and theoretically at least does not exist. Practically of course it does, after about 1880.
Because it starts with the letter "Z" it is safe to say it is not Greek, but obviously the family lived in Greece. The question is: What was the original name?
The closest name I could find are (My Database is the worlds largest): Zizinios (from Chios); Zizilas from Hydra; Zinos (Crete, Venice); Zinzi (Greece and Italy (Rimini); Zio (Venice); Sizi (Italy); Zissi (Greece) & Zissopoulos (Greece).
Only wives names will help you further. (To make things worse, Zizo is also a common name in North Europe, (Baltic States).
Regarding Panagiotis father's name, the answer is in hi brothers name: Euthymios Zizos, probably born around 1868.
Regarding the name Zizos, my guess is: The original name was "GHISO" (Plural "GHISI") (Lords of Tenos; Lords of Andros; Lords of Amorgos; etc etc.)