I am a US citizen and became married in 2007 in Japan where I have lived ever since then, and since I married in Japan I used my passport as identification. My passport has my last name misspelled and all my paperwork in japan is with that misspelled name. So my question is my marriage valid in the US with the false name even after I go back to the US where I have correct identification or would I need to amend my passport for it to become valid?

First it is not a "false name" if it is merely a mis spelling of your real name, The issue may be why you did not correct your passport which is suppose to be the correct government issues ID which requires a documents to get it.
So if there was an error.

If you were to actually use a false name, but you used your name as registered with the federal government

You in this case are legally married, and will have to get a divorce. You will need to correct your passport.

A big difference in false name, to a mis-spelled name

Well I understand I am legally married. But does the US recognize my wife as my wife in the US. She has the misspelled last name and if we go back to the US I would not.

Was the marriage valid in Japan? If yes, then all that will be necessary is to get the spelling of the name corrected.

You really should have corrected this error as soon as it was discovered. Even if you had to get it corrected at the U.S. Embassy in Japan.

Yes, a marriage that is valid in Japan is valid in the US.

You merely need to get the incorrect name corrected.