In a place as literal-minded and permeated by magic as the Discworld, the concept of the childhood imaginary friend or "inner voice", which on more prosaic worlds is an imaginative construct of the mind, becomes more than just imaginary.
Take, for instance, Agnes Nitt's alter-ego of Perdita. She exists, and has been known to take over Agnes whenever she gets fed up of being the thin girl struggling to get out from underneath the mountain of chocolate consumed by the plumper girl.
Consider also Rincewind's conscience, which pops up in extremis with a life of its own, and gently nags and berates, until Rincewind reluctantly does the right thing. Here is another entity that is clearly independent of its host, as Rincewind's concept of the "right thing" is to run away from danger, and keep on running, until he is either in a place of relative safety or is in danger of falling over the Edge.
A third example appears to have been created by Samuel Vimes in response to Vimes' inner musing on "who guards the guards", i.e., who prevents a Watchman from going over the edge and making his own law for the day. Vimes - with a little prod from Captain Carrot - resists the seductive voice of the Gonne, with great effort. But that seductive voice takes other forms and requires constant checking and total self-control. Detritus once remarked about the effort it took Vimes to arrest, rather than otherwise deal with, child-killers who kept a souvenir of their crime: he considered that had he, Detritus, not been there, only Vimes would have walked away alive. Vimes refers to the constant temptation to go "Dirty Harry" as "The Beast", and considers that if kept on a leash, it can be a useful asset to the watchman. In Thud!, we see both the Beast and the Inner Watchman take shape inside Vimes: one is the dread entity the Dwarfs refer to, when they have to, as the Summoning Dark, which seeks to take possession of Vimes. In response to this threat, from somewhere deep within Vimes, there emerges the personification of the Watchman: the Guarding Dark. This is the part of Vimes that has successfully resisted allowing the Beast to take over, and which appears to have developed a sentience all of its own.
Is Foul Ole Ron's Smell a fourth example? This entity is clearly more evolved than the person who created it and has been known to follow intellectual pursuits all of its own, such as visiting the opera or the art gallery. It certainly took a keen interest in the Patrician's collection of sheet music, until invited to leave the Oblong Office.
A close reading of Carpe Jugulum suggests that second personas are more common that would appear, at first glance. Granny Weatherwax, in an in-between state between death, becoming a vampire, and returning to the world as herself, is interested that the road back to the real world, as herself, is signposted by Mightily Oats's Omnian prayers. She is even more interested that Mightily is fighting a constant battle with his Inner Atheist, or at least his Inner Agnostic. For wrapped in the strands of prayer is a second Oats who is not religious, in fact fiercely anti-clerical and negative about faith.
Ah...one mind, split in half. There were more Agneses in the world than Agnes dreamed of, Granny told herself. All the girl had done was to give the thing a name, and once you give the thing a name you give it life...
And of course while in the near-Death space where the black sand is underfoot, Esmerelda Weatherwax comes out as Granny's dark shadow, to taunt her and seek to lead her into the other sort of witchcraft: "I've fought you every day of my life and you'll get no victory now. I knows who you are now, Esmerelda Weatherwax, and you don't scare me no more!"
This indicates that Granny herself once had a "Perdita" of her own to deal with... she has, in fact, admitted as much to Agnes Nitt, who, (like Magrat before her,) didn't notice or realise how privileged she was to get a very rare glimpse into Granny's deeper psyche. When Agnes arrives back in Lancre at the end of the events described in Maskerade and admits defeat - she agrees to move into Magrat's old cottage and "give it an airing," which is as good at conceding that she is ready to become a witch, without actually admitting it - Granny rewards her with a personal confidence. Like Agnes has a Perdita, Granny, at the same age, once experimented with being Endemonidia. Granny is perhaps saying, without admitting it, "I had a Perdita too, once. It's not unique."
Oddly enough, this split-mindedness has also been acknowledged in one case as a psychological disorder. In Thud!, the woman guarding the entrance to Mr. Shine's gameroom, under her rock shop, has two distinct personalities, Ms. Pointer and Ms. Pickles, which can apparently withhold information from each other. Ms. Pointer says, "It's supposed to be an illness, but all I can say is, we've gotten along well."