The Doctor vs the Doctors - individuality?

Each incarnation is a different persona. Same basic Doctor, but the settings of the personality are tweaked. It’s like how we change our personalities depending on age, circumstances etc, with memories and experiences filter through this lens. When we’re young we are more carefree, moody in the teenage years, stressed in times of hardship, blissful in marriage. Someone on the eve of their wedding or about to start uni could say they don’t want to change from who they have been. I’m not the same person I was five years ago, but five years ago me and now me, I am he and he is me and we are all together. If I traveled back five years it’d be The Two Omegas. The Doctor’s changes happen today involve a facelift.

For example, the War Doctor. He represents a time in your life you want to forget due to trauma, or shame. Maybe you lost someone or had a drinking problem, or got caught breaking the law on a serious charge. That’s your War Doctor even if you look nothing like John Hurt.

Well on one hand we have Deep Breath's broom analogy and on the other The Five Doctors' man a sum of his memories. 

I guess the middle ground is The Sirens of Time, some elements get switched around but the core stays the same. Perhaps that explains Time Lords' tendencies to pick titles, a set of core principles to anchor themselves to throughout their incarnations (perhaps indicating why the War Doctor's stopping of the title is such a fixation of his, he's purposely trying to distance himself from his core personality). The Sound of Drums does suggest Time Lords picking titles isn't uncommon, though clearly it's not something they all do. 

I’ve always thought of the doctor, or any time lords really, that when they regenerate every cell is replaced and renewed and this will also work for the brain cells. So when he regenerates his entire wiring changes but his/her memories are retained. And i think this is what makes the doctor the doctor, the master the master - their memories. It would be similar to if u were reborn but retained all the memories of your old life - it would catagorically be a different brain yet your memories will surely make u act similar to how you did previously even if you are wired a bit differently. So to actually answer the question, i think doctors can change dramatically between incarnations and sometimes they do, but their experencies keep them as the doctor.

P.s. i guess this is sorta the message tuat was going for that memeories are what make a person, which is interesting.