How to change author of history commits definitely?

I have created a personal repository (for practice and fun) since several months ago and I continue to develop it so far.
Recently I checked the commit history and found there were several commits made by using a wrong account, which is offered by my company and should be used for work. I have already tried the command below :

git filter-branch --commit-filter '
if [ "$GIT_AUTHOR_EMAIL" = "xxx@gmail.com" ];
then
  GIT_AUTHOR_NAME="another_name";
  GIT_AUTHOR_EMAIL="yyy@gmail.com";
  git commit-tree "$@";
else
  git commit-tree "$@";
fi' HEAD

After this command I thought it worked. I checked git log and the author has already changed.
But what confused me is that I can still see another name in commit history (shown as img below).
image
Could someone tell me what I should do to modify those commit records definitely ?

You need to change the committer email and name in addition to the author name. I’ve used this script a while ago where I needed to change both, too (just fill in name and mail):

git filter-branch --env-filter '

OLD_EMAIL="..."
CORRECT_NAME="..."
CORRECT_EMAIL="..."

if [ "$GIT_COMMITTER_EMAIL" = "$OLD_EMAIL" ]
then
    export GIT_COMMITTER_NAME="$CORRECT_NAME"
    export GIT_COMMITTER_EMAIL="$CORRECT_EMAIL"
fi
if [ "$GIT_AUTHOR_EMAIL" = "$OLD_EMAIL" ]
then
    export GIT_AUTHOR_NAME="$CORRECT_NAME"
    export GIT_AUTHOR_EMAIL="$CORRECT_EMAIL"
fi
' --tag-name-filter cat -- --branches --tags

As far as I remember that script needed to run on a bare repository. Using filters on a separate clone of the repository is good anyway, so you can easily recover in case of a mistake.

As for why, see Viewing the Commit History from the Git Book:

You may be wondering what the difference is between author and committer. The author is the person who originally wrote the work, whereas the committer is the person who last applied the work. So, if you send in a patch to a project and one of the core members applies the patch, both of you get credit — you as the author, and the core member as the committer.