|Ann Talbot (left) meets Nyssa of Traken (right) in Black Orchid|
It is generally taken that all fingerprints are unique, but - as I understand it - this isn't actually provable. For instance there is no global database of everyone's fingerprints... and fingerprinting was only suggested as an investigative tool in the late 19th Century. So who knows what the fingerprint swirls of past centuries or millennia were like?
Take this possibility to pulpy extremes, in a heavily populated universe as seen in Doctor Who, and the amount of travelling The Doctor does, and it's not surprising that every so often he bumps into people who look a lot like people he knows (or, even, at times, himself).
I'm not even considering here Time Lords who have adopted the appearance - upon regeneration - of people they have previously encountered (such as The Twelfth Doctor and Caecilius, or The Sixth Doctor and Commander Maxil), but characters that just happen to be lookalikes.
|Morton Dill from The Chase|
I'm thinking of Nyssa meeting her doppleganger, Ann Talbot, in Black Orchid; the striking similarity between American tourist Morton Dill - from The Chase - and The First Doctor's next companion, Steven Taylor; The First Doctor and The Abbot of Amboise, from The Massacre of St Bartholomew's Eve; The Second Doctor and Ramón Salamander from The Enemy Of The World; and David Bradley's First Doctor and Solomon the pirate from Dinosaurs On A Spaceship for starters.
|Solomon from Dinosaurs On A Spaceship|
Ignoring the behind-the-scenes logistical reasons why some of these occurred, "in-universe" they factor in nicely as a justification for a Doctor Who RPG gamesmaster to throw in characters that happen to look like one of the player-characters... but aren't necessarily manipulating that fact for evil intent.
As we've shown, there's a televisual precedent in Doctor Who for using this trope at your table (and you can, kind of, justify it with pulpy "science".)
It's a massive universe and sometimes these coincidences occur: misunderstandings, mistaken identity shenanigans, and wackiness ensues.
It doesn't have even to be a serious story element about the nature of identity; it can easily just be a comedic sub-plot.
While lookalikes certainly aren't a gimmick you should pull out too often, they make an interesting change from our old favourite: the evil clones from an alternate dimension (very topical in the wake of Crisis On Earth-X and just as Star Trek Discovery plunges gung-ho into the Mirror Dimension).