That "killing people in the shadows" is just one interpretation of the word. While it is the one most commonly used in the gaming world, it is also the one least used outside the world of gaming. Assassination can also mean to kill a person who is a public figure, or to kill for ideological causes. It suits fine, I don't think it needs a change.

I don't quite see the connection with greek mythology, beyond the use of the word pantheon. Can you explain further?

Yeah, but most cultures have some gods and heroes. What makes you think it's SPECIFICALLY ancient greece? Just sounds a bit far fetched. If I remember correctly, the demigods in greek mythology were mostly given that "title" because they had one mortal and one immortal parent (or a god otherwise helped out at conception). In this game, they are mortals who have grown so powerful through impossible deeds or misdeeds that they simply cannot be compared to other beings in this world (and when the one true god disappears, they all want to take his old place).

Anyway, point being, demigods are not only found in ancient greece but in judaism, christianity, buddhism, celtic folklore, norse mythology and so on and on.

Haha you just made me LOL

It does not have to be Greek. That is just what comes to mind for me given the official name. There are many mythologies to pull from. I am curious on how using Greek words would be counterproductive however.

the day I could understand you at all

I thought assassin was really weird at first, but I can't think of anything else that fits, and I'm used to it.

Current usage of "Assassin" is anyone who trains specifically for the purpose of taking life with efficiency.  No one is saying Rook has his roots in an ancient sect of drugged fighters, but they spawned a word which works to describe him, because they do the same thing.  Methodology varies, but killing is the tie that binds a walking castle and a fallen angel...