Hi Murali,
Your repository is secure. This message indicates that the author of the commit has not set their username correctly. It has no bearing on the authentication required to push the the commit to Bitbucket - in other words, it was pushed by a user who has permission to push, but that info just wasn't synced up with Git/Mercurial itself.
The user needs to set their username using this guide: https://confluence.atlassian.com/bitbucket/set-your-username-for-bitbucket-cloud-actions-272597445.html
Hope that helps!
Alastair
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