You can buy a legit passport in St Kitts & Nevis for around $400K. It's about $50K for the application and then you have to invest $350K in govt approved real estate developments, so it's not like it actually costs the full $400K - you should make some money back from the real estate part.
There are a bunch of methods based on getting a completely fake identity such as the infamous "day of the jackal fraud" based on the the Frederick Forsyth novel Day Of The Jackal, where one character gets a replacement birth certificate for a dead baby and then builds a whole identity around it. Apparently this is still possible in some countries, but it all depends on your means, accent, what country you want to do it in etc.
Another alternative is just to take a heap of cash to a third world country and buy a legit passport in whatever name you want from the authorities. But you would have to meet the right people etc.