Not very much, this is one reason I am reluctant to even call that child me.

Well, this is not a binary per se. In a sense it is you but in another sense it is not. That's a short answer. But one thing indisputable is that you are in the same body this supposed other thing/person has previously occupied. Which isn't the same thing, but if two people can occupy the same body at different times, i am not sure the same person and two different bodies is that far of a stretch.

While this sort of categorizing is useful for brain functionality, it doesn't seem to reflect anything objectively real or unchanging. It's like when somebody refers to say, google chrome, is a new version of google chrome different from the past versions?, we still refer to it as the same thing and say it's "changed", but in a literal sense it isn't really the same browser.

Whilst I agree, my problem with this is that if we apply this exacting condition on sameness, then the word becomes meaningless. Because literally, given that matter is only attenuated by c, then every moment implies that you are a new person because your experiential mix (or function, summation, total, or whatever term) changes every moment.

In this sense, there is no anchorage for personhood. But we distinctly perceive this not to be the case. That is, we intuitively ascribe to continued personhood irrespective of changes.

I'm not sure there is such a distinction in the brain between memories and the "program", unless you're referring to personality and values.

This is implied but can be argued out. You don't recall every last one of your experiences, yet you are some function of them. The function is a result of and not necessarily tied to your experiences. That is, if your experiences generated your character, does eliminating the experiences eliminate your character? I disagree since I can hardly recall what I did yesterday. But it surely must inform where I am and what I am like today.

Well yes, but this program that causes one to act differently to different data is just the personality, which we already established can also change during a lifetime.

Yes. It changes. And as a function of experiences. experiences which are collected over a lifetime or time period. Everyday it is added to. Starting a new lifetime will just be continuing the addition process. What causes changes in one lifetime? A powerful experience (death, love, loss, etc). If we change through these in one life time and distinctly feel we changed but we are still ourselves, then the same should apply after such a process as reincarnation.

The whole situation is very messy, but in the end, I think the memories are the closest to it, as I identify with those memories as being me, if I had no memories I wouldn't know who I was before, and even if being told about it, if the memories were properly gone and there were no remnants, I wouldn't identify with these stories from other people about what my body had been before.

Interesting. What about things that you do? Things that you like/dislike? Your behavior etc? Do you feel those will change if you have a memory loss? If so, why/why not. I have no doubt that some of these will change. But not all! And these are the things which are ingrained deeper. Such as virtues/vices, propensities etc. Example, a wickedness, cruelty, generosity, kindness are traits which, though are formed through experiences are not attached to them. This is because people have come to do them not because of some memory but because these are things they want to or enjoy doing.

I feel that a memory loss will make a person not remember what they liked doing. But upon a chance exposure to this same thing, the desire for it will reawaken. But until such a reawakening, it will simply persist as some subconscious longing. Like something was missing without knowing what it is. ... depending on how strong the propensity is.