First I'll say that this in the area of things that "I know I don't know." But I do have preferred models until I find it to fail in some test.

Personally, I like to think that the 'essence' of who we are is more in the pattern that is setup within the biological brain/body. So If this same pattern were to be transferred into something purely mechanical, including both the brain equivalent as well as analogous pain, temperature, etc sensors that the biological body has. Now trying to also include something for the concept of hunger/thirst is where I start to question this ability, since machinery/robotics don't necessarily get energy from food nor require water to hydration (that allows molecules to move around.)

In the end (sry for the shpeal there) I see the biological body as a mean to capture a pattern of energy (not one to one like reincarnation, but rather a scoop from the ocean of stuff comprised from lots of these 'dissolved patterns.') While alive, we can slowly change this pattern internally over time. After that, it can only happen from outside forces.

I still love this model from Babylon 5 that is similar, using the term of the 'soul.'
https://www.youtube.com/watch?v=pzag71pOG1s