The old username will no longer be tied to the user, so anything which uses it (like old commit messages) will no longer associate correctly. (And, if you give a user a username which some other user used to have, username lookups will begin returning the wrong user.)

It is generally safe to rename newly created users (and test users and so on), but less safe to rename established users and unsafe to reissue a username.

Users who rely on password authentication will need to reset their password after their username is changed (their username is part of the salt in the password hash).

The user will receive an email notifying them that you changed their username, with instructions for logging in and resetting their password if necessary.