People think that combining minds would be something like one mind taking over the other, or a mix of the original and the incomer, with the incomer being the main personality.
It's not. It's really, really not.
What's happening is entirely physical. No psychic power or magic or jiggery pokery or anything else. No, it is, at its most basic, two electrical systems combining into one.
Now, if you have any knowledge of how computers work, you should know that combining two systems into one just doesn't happen. Not exactly, not electrical impulses being laid over one another to the very wire.
That's just how it happens, though. The chances of survival are slim to none, unless one particular thing happens. Keep in mind that memories are always stored in different places, different neurons and synapses, even if in the same part of the brain. And if, by any chance, memories don't overlap, that helps keep both personalities there. But that's only if the core of the mind overlapping with itself doesn't fry the entire brain within the few seconds it would take to create this hypothetical double-person.
Which means that one person's very core of their mind, their instincts and their actions and their movement, have to be dulled enough that the electrical impulses only strengthen enough to be more compulsion-friendly and animalistic, rather than strong enough to absolutely fry one's mind.
So, in this hypothetical situation, let's take a memory-full, extremely intelligent old person who got in a terrible accident and is now near-comatose, stuck in their own mind for their basic, instinctual part of their mind no longer works, but their memories and intelligence stay put, leading to a very imaginative, very dead-to-the-world, person. Then let's take a very simple, memory-absent young person who does stupid things on a whim and is very emotionally there.
Now that we have two unwilling subjects, let's say that these two people are from different places, different worlds, maybe even different dimensions. Let's say they're as close to exact opposites as one gets, even.
In this hypothetical situation, the electrical impulses and mind of the veggie just so happen to be sent through the void, entirely by accident, and entwine with another mind that just so happened to go through the void. Suddenly you lose two people, and gain one who isn't more one, or more the other, but is both, combined. Two people are dead, and one is born.
One very confused, intelligent, fit human being that has the memories of two opposing people who say that the facts in front of them are totally, illogically possible.
Only, this isn't a hypothetical situation, the one thinks. No important memories were fried, though the one can't recall any scent or taste - or even generalized sound - at all. So the one, that has decided that it is a she, is very confused when sounds bombard her. Sounds that she understands, but has never experienced before.
Explosions. A voice asking if one half of her was alright. One part of her.
A warm, golden smell. Coppery, iron-scented smells. An engulfing, empty smell. The smell of time. The smell of metal. The smell of the void. The taste of the place she was in. The smell and taste of the one who stood before her, looking increasingly more and more worried.
The man before her smelled nice, and tasted much the same. She could taste his smell. She was vaguely reminded of how snakes work. Half of her loved snakes. The other half didn't dislike snakes. The one decided that she liked snakes. Snakes were cool.
The man called to half of her, and she decided then and there to make a name for herself. Or, perhaps, the man before her would name her? Half of her was sure he'd understand the situation, but the other half warred, and thought that he'd try "fixing" her, try erasing one part or the other. The one decided she liked existing. The one also trusted the man before her with both parts of her life.
"Rose! Rose, are you okay? Rose, answer me!" The man repeated, looking into her vacant eyes. Her vacant eyes that were no longer vacant.
Most of her memories were of her thinking, of her being in her mind and creating scenario after scenario to ease her boredom. Most of her memories said that she was a very introspective person. It makes sense she'd immediately go into her own mind when confused to try and figure things out. Now that she had figured things out, she came back to the world of the living, and focused her eyes on the man.
Most of her just wanted to go along with it, to pretend to only be Rose. The part that actually was Rose, part of the part that was once Rose to be more specific, rebelled against that idea, wanting to be her own person.
"Sorry, Doctor." The one apologizes. The one apologizes for being more than Rose, for no longer being Rose despite being in her body.
"Rose! I thought I lost you for a moment there. Are you okay?" The man she knew as the Doctor asked. The one frowned, understanding and empathetic towards what the Doctor might feel when she tells him.
"I'm so sorry, Doctor. Rose is gone."