Since this is CyberPunk, there's always that chance that you can flirt with not only death, but almost immortality, given that you're rich enough. This concept is explored widely in shows such as Ghost In The Shell, and Altered Carbon - and it can happen here, as well. However, because of the open-ended nature of this type of occurrence, it's necessary that we've created a guide, for how this sort of thing is supposed to go down.
First things first, honestly, the only people who should be performing this procedure, are individuals who specialize in it. This isn't a service that a typical Augmentation Doctor, or RipperDoc can do - this is something completely separate from them, since this is a very high-end, and technologically advanced procedure.
Every legal citizen of Cascadia is outfitted with the Arch - which is a small device installed at the base of your skull, that simply put, basically acts as mediator between augmentation, your brain, and your body - which is primarily why modifications that affect the way your brain function are made specifically to your Arch, and not your brain.
Your Arch contains everything about you - after all, it's yours, you can't take it out, you can't have it removed - if it gets damage, you undergo surgery to have a new one installed. It stores everything about you in the CCDB - Cascadian Citizen Database.
There's a few different ways you can go about brain or body-jumping.
You could either simply be "sleeved" to a pre-existing synthetic body, which happens by using something called a 'SomaSleeve' - which essentially is almost like an SSD for your soul. A technician essentially "writes" your entire being to your Arch, which is then copied through your Arch to the the SomaSleeve. They take the SomaSleeve, and re-write it to an Arch in a synthetic body - this is called going Synthetic. The major issue about this, however, is that when you go synthetic, this drastically reduces your capability to naturally learn new abilities and skills. You're also not a human anymore, at that point, and experience all of the major downfalls of completely losing your humanity, which personally is a little bit depressing, but you might think differently.
If you're sleeved, your original body is essentially a vegetable. At no point in time, are you 'Cloning' yourself. You can either opt to have your organic body disposed of by whatever means are offered - cremation, burial, woodchipper, shoot it into the sun via mass-driver, whatever. Or - given that you're rich enough, you can opt to have your organic body cryogenically frozen, for future use.
However, you could always purchase a CyberBrain - which run extremely expensive. Overall - a CyberBrain is simply a safer way of doing all of this, and there's always the ability to retain your body, and use your CyberBrain for insurance - as in, if your body is destroyed, as long as your brain isn't, you can stay on your grind. You're also able to entirely swap bodies with another organic body, although this is extremely illegal, although usually hard to prove. Even moreso if you don't re-write the Arch of the organic body you're moving into.
Essentially, when this process takes place - it must take place over the course of any time that isn't complete all at once, largely because you're supposed to be replacing the major parts of the brain, one-by-one, while giving the rest of your brain a chance to get used to the fact that you just swapped out a part of itself with what is essentially an extremely powerful computer. This method is largely effective purely for the idea that you have nearly perpetual life insurance at this rate, and essentially, an extremely fragile state of immortality.
You still have the option of having a CyberBrain transferred to a synthetic body - synthetic bodies come with a blank Arch. It's simple enough to transfer the contents of one Arch to another, so what needs to be done is an entire replacement of the brain into a new synthetic body. Of course, there are two types of these synth bodies: one that supports only the SomaSleeve, and one that supports the CyberBrain. The upside to doing any of this with a CyberBrain, is that you retain your ability to be completely human, for the most part - your brain is just as human as it was, but now parts of it are augmented. The CyberBrain still functions the same way, it still learns, processes information, and retains your personality and what makes you you.
Keep in mind that this isn't just some off-handed procedure for fashionable purposes.
When you're having your brain replaced, or you're moving to a new organic/synthetic body, or you're being sleeved - you're changing your entire life, your entire existence, your literal position in the current mortal coil. You're riding the cusp of what it means to be "alive," and there are extreme philosophical implications that come with this - since you are now quite literally, merging your existence into another thing. This type of event, this type of RP is meant to be a life-changing experience for your character - and should be treated as such. Not only does this defy what makes humanity humanity, it quite literally ushers in what is the developing stages of transhumanism. So - treat it like so. It will leave a lasting emotional impact on your character, for better, or for worse, and should be something that they consider the implications of for the rest of their life, no matter how long it may be.