Disappearing isn't the hard part, it's re-integrating with society. You'd have to create an identity from scratch that lines up with your apparent age. This is not cheap currently, is not legal, and will only get more expensive and harder to do in the future as surveillance increases, to the point where it's basically impossible to forge a phony identity.
You also have to do this every 20 or so years due to a static age.
Surgery? With what money? Thinking of having an investment? You'll need some sort of identity to invest and you won't be able to carry it over from one identity to another without fully liquidating it right before you die. As mentioned, most if not all your investment would then have to go to creating your new identity.
Maybe you think you'd be fine being a nameless person. What's the point in immortality then? You can't enjoy society without having an identity, can't get a decent paying job, and as such cannot reap the benefits of a prolonged life.
Money would be a trivial problem for someone whom has knowledge and experience from ages. Look at the world around you today, and you will see many people scoring large amounts of cash for putting to use, or coming up with ideas that seem to be staring us right in the face. Justin Bieber has made more than 50 million dollars so far, and Notch gets a nice amount of money to. How hard would it be for someone whom has such a wide array of knowledge to come up with an idea that makes him alot of money to.
Of course, the popularity would probably cause a problem in terms of disappearing from society, but it would not make the task impossible. Once more, I bring about the faking of death procedure. But you do make a good point, disappearing isn't the hard part, re-integrating would be.
Chances are if you are going to live forever, you will eventually find out how to make a fake identity for yourself. Really, it's a simple matter (when compared to the large amount of challenges one would face for eternity) of figuring out how to make the paper-work you need look legit, and finding a way to make some people confirm the fake identities life to any employers.
But, even if what I say above is not exactly the wisest route, there is still the fact that I have all eternity to plan out how to make it work. Give a guy enough time and knowledge, and he can do whatever it is he wants to do.