Git records an author name and email address whenever you make a commit. That is configured locally, so maybe the data there is still from when you were using your old account? Here’s the Git Book section on how to configure your identity, that should do what you need in principle.

Two Github-specific notes, though:

1. Github uses the author email to detect that you made the commit and connect it to your account. If you want that (I assume you do), you need to either use an email address that’s on your account, or if you want to keep your address private you can use a Github-provided no-reply address, see About commit email addresses. If Github recognizes the address it always shows your username instead of whatever author name is in the commit.

2. It is technically possible to change the author information in old commits, but that will cause chaos if anyone else is using the repository, because it changes history.