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In the registration messages, the Drupal core new user messages is like
Thank you for registering at [site:name]. You may now log in by clicking this link ...
After setting your password, you will be able to log in at [site:login-url] in the future using:
password: Your password
And shoud be:
username: [user:mail] (also you can use: [user:name])
I tired to use hook_mail_alter() but the [user:name] tag is already replaced by the username.
I don't know how to "catch" [user:name] in the message before it is being replaced. If someone helps with an idea I can make the patch.