just my 2 cents worth.
Mythology is a slightly misleading term really.
Sometimes we use the term mythology for a fantasy theology. The gods were in the myths, so studying gods is studying myths. Ok I get that but the superorganised world where the Gods are known (by the GM) really is a study of theology. The primary source for theology might be myths or a sacred work.
But from the players point of view wouldn't it be better to have a mythology (Stories of the epic adventures of so and so and some god's relationship with so and so.) Myths in this setting often are told and retold and they contradict themselves a bit sometimes. But that doesn't really matter.
Even in Christianty, where we understand a lot of theology from sacred writings people are obsessed with making it all into a system that we can understand. When some things are simply unrevealed.
Point is even if the god exists could your average human being understand how he/she thinks or can they see the big picture.
I like the idea of using similar names to real world mythology, mainly so I can remember who is who! I found this working on Helena, that related names or similar names really help. Gods in mythology often represent certain character traits so once you get the name and traits sorted it doesn't really matter what the real world mythology exactly was. (For example I called the town and oracle in Helena Pythia. The oracle at Delphi was the Python, the games held there the Pythian games.)
You could use names which work for you only to. The Helenic god of the sea I called Thelassion (ancient greek word for sea) but its all purely for my personal memory
I noticed that pbj did something similar in his campaign he posted recently.
The other thing I like about using a quasi real world example is that the word itself is a symbol and it comes with a lot of baggage that helps communicate a lot about who we are talking about. Zeus is foreign to us but we know lighting bolts, big beard, looking down from on high. Aphrodite? Mars (Ares)?