- There were 108 suitors (we know this from the Odyssey 16.245-254 [1]).
- All that Homer told us is: They were gladdening their hearts at pessoi in front of the doors, sitting on the hides of oxen which they themselves had slain (the Odyssey 1.106-108 [2]).
- You can't have 108 sitting men play the same game of marbles.
IMHO, pessoi was a 1:1 game and it was not a board game.
[1] https://www.perseus.tufts.edu/hopper/text?doc=Hom.+Od.+16.24...
[2] https://www.perseus.tufts.edu/hopper/text?doc=Hom.+Od.+1.106...
Like you wouldn't call (Kievan) Rus' "ancient Russia"
Persia as a word for the whole region is an exonym, derived of the name of a single province and the people who lived in it. Iran is the endonym that the people living in the area have understood to refer to the entire area for millennia.
It's like calling the Netherlands Holland. Everyone understands what you are talking about, but it is definitely not very precise, and some people from the region might take an exception to it. Fine for conversational use, not so much in academic literature. You might talk about the Persian Empire when referring to the Achaeminids or the Sassanids, but that comes with the understanding that while the ruling class is Persian, they rule over an empire of people, many of which are Iranian but not Persian.
When talking about ancient people and countries, it is hard to avoid using exonyms, as they are usually much better known than whatever names may have been used by natives. In many cases such names have been discovered only relatively recently, during the last century, so they are known mostly by professionals and they are rarely found in popular literature. Moreover, frequently for the native names there is a much greater uncertainty about their original pronunciation than for exonyms.
not exactly. Persians are also majority of people in what's now called Iran (just like Russians are majority in Russia, this is the same naming pattern as for many countries) and renaming is a result of an invasion. Talking about "ancient Iran" before it Muslims arrived is talking about Persia