Let me explain.
It sounds weird as a title, but it's quite literally that. The identity is to have taking ones place, instead of rejuvenating which is a side effect, taking one's look and then memory comes in charge, altering whatever memory you have of the previous individual's identity.
We have different clues throughout the manga, the most obvious one is disguises. Disguising, taking someone's place, the fake identity to build from scratch (Araide).
The FBI protection program, starting your life all over again by changing identity everytime they get to you and hiding for life.
Sharon Vineyard -> Chris Vineyard
Haibara's "it's like the Japanese dolls" comment. Not everyone is into it, very few people is interested in whatever she was making. Changing your appearance to assimilate one's "DNA" or one's appearance, bringing the dead to life through your own soul and body. Not a whole lot of people is interested in that, but it's special to criminals/someone seeking revenge/a wolf/a silver bullet/a detective, huh?
The halloween party!
"You can't go against the stream of time" -> distorting timelines and memories of one's identity. Changing the course of events by taking someone's place, it's impossible, but if it were to be, then punishment will surely befall whoever tries to do so.
Shinichi Kudo -> Conan
Shiho Miyano -> Sherry -> Haibara
Akai Shuichi -> Rye -> Subaru Okiya
Furuya Rei -> Zero -> Amuro Tooru -> Bourbon (bruh)
These are all alter-egos, different identities that, based on the situation, cannot interact due to personal reasons, be it regret, fear, hatred, danger, trust issues and so. One can recognize the other, but what if all the wrong identities meet at the same place for the wrong reasons and wrong timing? Wouldn't it be easier or nice to have their memories altered? Erased? Factually wrong?
All of this is connected to the Itakura prog.
Another interesting point is >!Rum's special ability of having a scary photographic memory and recognizing people, yet as a 2nd in command doesn't know a flipping flying shit about the boss!< and >!wants to ingest the drug to reverse whatever his eye was. !<Another interesting comment he made >!was "a dead person wouldn't be present at reunion, would they" referring to the Akemi Miyano capsule case.!<
I wrote this on a whim and rush as I'm headed outside, but I had to lay it out before I forget and read what you all think.
I hope it makes sense, and I apologize if some quotes are not word by word right. It might be messy, my brain is scraping info around. I hope it's "clear" in big terms.
Yup😁