NOTE: This answer changes SHA1s, so take care when using it on a branch that has already been pushed. If you only want to fix the spelling of a name or update an old email, Git lets you do this without rewriting history using .mailmap. See my other answer.
First, if you haven't already done so, you will likely want to fix your name in git-config:
git config --global user.name "New Author Name"
git config --global user.email "<[email protected]>"
This is optional, but it will also make sure to reset the committer name, too, assuming that's what you need.
To rewrite metadata for a range of commits using a rebase, do
git rebase -r <some commit before all of your bad commits> \
--exec 'git commit --amend --no-edit --reset-author'
--exec will run the git commit step after each commit is rewritten (as if you ran git commit && git rebase --continue repeatedly).
If you also want to change your first commit (also called the 'root' commit), you will have to add --root to the rebase call.
This will change both the committer and the author to your user.name/user.email configuration.
If you did not want to change that config, you can use --author "New Author Name <[email protected]>" instead of --reset-author.
Note that doing so will not update the committer -- just the author.
If you just want to change the most recent commit, a rebase is not necessary. Just amend the commit:
git commit --amend --no-edit --reset-author