History combined with technology.
Now, they may not know exactly where in each incarnation's timeline they're meeting a given version of the doctor, but it isn't difficult to gather data about the same enemy fucking with you over and over again.
Any time the doctor goes back in time and directly encounters a given enemy, they now know that version of the doctor. Since we know, in canon, that the enemies have teamed up multiple times, and shared information to do so, it isn't a stretch to say that it's likely they've been doing so off and on as far back as the doctor's first visit to the most distant past.
Remember when humans have kept an eye on the doctor? Even on earth, with far less advanced technology than a species like the sontarans, they managed to be able to at least figure out that he was on earth a few times, if not exactly immediately.
If a given version of the doctor doesn't behave in a way that indicates that he/she has experienced a given event, you can make a rough guess which order each incarnation came in, if you keep track of your encounters.
In universe, the doctor is one of the most famous individuals ever. Known and recognized in a wide range of times and places. But he's really only recognized by people that encounter him as an enemy, because they're the ones that deal with him in multiple times and places.
A race like the daleks could easily crunch some data and figure things out, without the need to hand wave anything.
That's actually the least hand-wavy part of things, imo. You ask me, the real question is why there isn't a giant bounty on his head across time, with kill-on-sight orders propagated by his more violent and malicious enemies. You'd think that the daleks would simply determine that a doctor is present, and just go ham until he's dead. And then keep exterminating until he stops coming back.