Check your git credential helper: this is what has cached the wrong credentials.
git config credential.helper
On Mac, just open your keychain access->search for github.com related file->and edit credentials there.
See "Updating credentials from the OSX Keychain"
On Windows for example, that would be the Windows Credential Managers.
Open the Windows Credential Store, and see if the first user is registered there: delete that entry, and you will be able to authenticate with the second user.
(Here is an example for BitBucket; the same idea applies to GitHub)
In command-line, as seen here:
git credential reject
protocol=https
host=github.com
<empty line here>
and then to set the new username & password:
git credential fill
protocol=https
host=github.com
<empty line here>
Type git help credential
for detailed info.
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