Observable similarities are probably the easiest problems to solve. A hair-dye / new hair cut, a few wardrobe changes, and moving to a new city will solve your problem of someone observing you. Of course, this means never forming long-term bonds. You'd have to maintain only casual acquaintances at most, as you'd need to sever ties every time you relocated. And no facebook or similar social media connections, either.
You'd also want to minimize your odds of being recognized later. So you would need to avoid events that might be photographed or televised. It would be a bit uncanny if some B-reel footage of historical event X had you in it, and someone was like, "That person looks just like you!" No getting involved in big political rallies or buying front-row concert tickets. A low profile is the way to go.
Wealth and possessions would be a bigger problem. You would need to have some sort of "foreign corporation" or blind trust or something that owns all your real property. Stocks, bonds, houses, etc. on multiple continents. You'd need to build a dizzying array of holding entities so you could, eventually, return to that property later and not be a penniless vagabond. You'd also need some carefully hidden archives to track where and when you've lived. Wouldn't want to accidentally return to your posh, NYC apartment too soon. You'd need to have several law firms on retainer. They'd need to be in the dark, too. But they'd be responsible for managing the properties, hiring servants to care for them, etc. And for managing your trusts/holdings. And for adding and removing temporary identities from the trust so you'd have money when you needed it.
You would want to have stashed things on multiple continents, so if something goes bad, you can run to a safe-house and not be stranded without money or passports. You'd want passports that were fresh enough to be usable, in case events required a hasty exit.
Legal identities would be the hardest part. You'd need to come up with a way to generate legal documents every time you moved. For a new person. They'd need to be more than just fake papers, too. We're talking basics like drivers licenses / passports / social security numbers (or equivalent in other countries). Because those are the basis for owning things. And for building a credit history for that identity so you can then pass background checks and travel freely. You'd probably have these identities employed by your fake corporations to justify the income levels. So you don't have to pass the kind of background checks human resource departments conduct -- you don't need valid college credentials or past employment history that is real. But you need to make sure that you won't be stopped at national borders. Or if you are, that your papers will pass official scrutiny. So they can't just be forged documents.
Self control and planning are key to the above things being built out over time. And for maintaining all of it for the long-term. Rash decisions and poor planning would be costly mistakes. From time to time, you would have to shift ownership of subsets of your possessions from one trust to another, from one law firm to another. Have your existing lawyers sell that NYC penthouse to an unnamed buyer (with hints that it is someone famous who doesn't want to be bothered maybe?) from a fresh, new, major law firm hired by you under a different identity. That corporation that owns your some part of your business interests is bought out in a hostile takeover by some new corporation (that you also own). This way, you can close out the books and there's not some strange paper trail that goes back hundreds of years at that one law firm. Because your lawyer might get curious and learn too much. And you'd have to watch all of these things, somehow, to make sure you get out of some bad investment before it goes under. Or that your possessions don't vanish from under you.
It would be a hard, lonely, job.