How do I change my name on a credit someone else has added?

Edit the relevant project, find the credit and change it to your name.

You should also send evidence it is your name on the credits using this form:

http://www.imdb.com/helpdesk/data_ver...

edit: Ignore this and see the post below:

MayorDefacto contacts me about this, as there is information I was unaware of (making my previous post invalid) and he has supplied a lot more information, which should help. Quoting him in full:

Due to the nature of this credit on Human Nature, Jo may need a bit more of an explanation. She said, "a production logged me as John Watkinson". True, but where they logged her was in the credits of the film, i.imgur.com/IrKESW2.jpg. That error was just copied over to IMDb along with teh rest of the credits. The name, John Watkinson, has two IMDb credits, imdb.com/name/nm0914442/. Since she used the singular "a production", I have to assume that the other (producer) credit is valid for someone named John Wilkinson.

This is a simple edit along the lines you explained, but Ms Watkinson should be cautioned to include an (as John Watkinson) attribute, and if this person, imdb.com/name/nm5821520/, is not her, the Roman numeral II to distinguish herself from the other person named Jo Watkinson. Failure to include the Roman numeral only moves the error to a different name, and not including the attribute invites anyone checking the title to correct it back (hopefully to a different Roman numeraled John Watkinson).

If she is the Jo Watkinson already listed, noting the credits error in the attribute should be no problem. If on the other hand she will be Jo Watkinson (II), then her explanation for the change should include words to the effect that she "will be using the name 'Jo Watkinson' for all future credits". Per the submission guide for names, imdb.com/updates/guide/names_all#primary:

General Rule: The primary name for a person in the IMDb is the one by which they are most often credited.

John Wayne was once credited as Duke Morrison, and even though that's closer to his birth name of Marion Michael Morrison, his primary name in the database is John Wayne.
We make an exception to the rule if we have reason to believe someone will be using a different name for all future credits. For example, if they changed their name because of marriage or have registered a new professional name with the relevant guild.
Such changes are made only for people with active careers. In the past, we required at least one onscreen credit with the new name; while that is still preferable, it is no longer a strict requirement.

Pertinent bits hi-lighted. Without that statement, IMDb will prefer the credited name even if it's wrong. Additionally, the final bit in the quoted section referencing "active careers" suggests that the name might revert back to John Watkinson (hopefully John Watkinson (II)) should she not have any future credits listed as Jo Watkinson.

Quite a lot to take in, so if you have any questions fire away and we'll do our best to answer them (also MayorDefacto will be watching over us, I'm sure).