There is only one real answer here, and it comes down to what it means to exist as a person. Passing on is consistently described, by all the people that have ever had near-death experiences, as an easy process that involved no big changes in how you experience things.
You’ve existed in a dream right? There’s a process of falling asleep and then you suddenly find yourself in the dream. You spend hours dreaming, every single night, then awake to find yourself back in the physical world again.
The afterlife isn’t like dreaming. Dreaming itself isn’t much of an existence, even lucid dreaming. Existence as a human has a very very large number of prerequisites. We are social creatures, deriving the meaning of our existence in relation to others. We can think, process, make decisions.
Sure, any of these things can be taken away from us, but it’s a continuous process. We never experience a completely sudden shift in everything. Even in the most dramatic case you can think of, let’s say a huge blade chops you in half at the waist all of a sudden and you manage to survive, you’re still you. Your self-conception would adapt to now being wheelchair-bound, but the continuity of you is preserved.
Physical death itself is a very slow and continuous process as well. Brains can take many hours to stop generating electrical activity, even with no fresh blood flow. A French chemist was able to keep blinking, by some accounts, for 30 seconds after he was decapitated.
So going by all this, one can come to a spiritual law, given everything that happens here, that one can never lose their entire identity, all at the same time. Whatever it is, it has to be gradual, with our sense of self having room to accommodate to the change.
And so when we die, we simply feel like ourselves in the afterlife. We have bodies, minds and spirits. Those bodies, minds and spirits, are just untethered to the physical plane. Eventually we come to adapt to the new spiritual world we’re existing in.
One mystic, Emanuel Swedenborg, described meeting people in afterlife who were atheists just like many people here. Even faced with the abject reality that they had had a physical life, then died and found themselves in the afterlife, still failed to connect the dots and realize divinity. One’s beliefs affect everything about one’s reality there even as they do here. What you believe becomes your reality, and this is one way we can posit God’s existence even in the absence of evidence. Believing in God makes Him real.
Recognition of others, in the afterlife, and indeed all manners of perception happens through a process of correspondences. Spiritual reality abhors falsity, in the absence of physical reality to hide behind, all persons become what they believe, and since belief becomes truth eventually, in the afterlife we become our self-beliefs. How we see each other similarly relies on those beliefs. Once in the afterlife, you’ll meet your friends and family you knew, and while they may look different, they’ll still present to your perception according to your beliefs of them. And since those beliefs commingled yours and their essence, that shared belief-reality will be eminently recognizable in the afterlife. Your perception of yourself may be different than other’s perception of you, but that never stopped anyone else from recognizing you right here right?
To further hammer the point home that recognition isn’t physical, two people, if separated for enough time, can “grow apart” to the point to where they’re unrecognizable to each other. And if there’s deep personality changes, say through brain damage, that lack of recognition can happen much faster.
To sum up, physical reality is and has always been a crutch, an illusion, hiding the more solid and real world of belief and spirit, away from us. In the afterlife, that crutch goes away and we experience life more authentically.