I assume “d” and “k” mean some kind of amateur “dan” and “kyu”, but I have no idea what “p” stands for.
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professional, i think.
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Yes, 9p would mean professional 9 dan, not just on OGS though, it’s very common I’d say.
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d and k
The d and k indeed mean dan and kyu, and those are automatically computed by the server based on the player’s wins and losses on the server. The dan and kyu ranks are somewhat of a universal system, but each go server and each national association might have their own way of computing these ranks, so the correspondence between OGS ranks and real-life ranks and other-servers-ranks can vary a bit.
Dan and kyu are a convenient unit for ranks as they correspond roughly to handicap stones. If you play against someone who is 3 kyu higher than you on 19x19, you can play with black with 3 handicap stones, meaning you get to play 3 moves before your opponent makes the first move.
Beginners start at 30kyu, then progress in reverse up to 1kyu, then 1dan, then up to about 9dan. I think in real life, in Europe the amateur ranks are technically capped at 8dan; and on the internet, depending on the go server it might be possible to go higher than 9d (I actually don’t know about OGS, I haven’t met so many high-dan players here).
p
The p means professional dan, and those are given to players who are known to be professional players and reflects their official professional rank in real life.
About the correspondence in strength between professional dan and amateur dan: very roughly, professional 1 dan corresponds to around amateur 7 dan, and then a difference of 3 professional dan corresponds to around one handicap stone, so that all professional ranks correspond to around amateur 7d-8d-9d.
Relatedly, one of the most important Japanese tournaments for professional is called the Judan, which literally means 10 dan. So, the professional dan rankings only go up to 9 dan, but if you’re the strongest player in the country you can win this tournament and people will call you “10 dan”.
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