New answers tagged terminology
Bouncing on @rainbolt's answer, if spatial position is not important in the game you describe but you fear confusion by using A,B,C,D,E or 1,2,3,4,5, you could maybe also go with the Greek alphabet : alpha, beta, gamma, delta or epsilon (or the symbols if you think people are familiar enough with them)... An alternative I sometimes use when I need to ...
I don't think there are any usual terms. This is not as fancy as cardinal directions, but it is simple: One Two Three Four Five The beauty of this approach is that, like cardinal directions, as soon as you know one position, you can easily identify the remaining positions. Granted, you have to know whether the numbering is clockwise or counter-clockwise ...
I don't know of an "usual" way of calling players in that case, but wouldn't a clock analogy do the trick, here? You could have: 12 o'clock 2 o'clock 5 o'clock 7 o'clock 10 o'clock
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