Hi @S, Srinivasan ,
I believe the "Just me" is not a feature, rather than a bug, but it may happen under various of different scenarios, you can read more here:
https://techcommunity.microsoft.com/t5/microsoft-teams/chat-quot-just-me-quot/m-p/357034
There's an on-going uservoice feedback about implementing the ability to chat with yourself in the link below which you can vote on, if it's a feature you want:
https://microsoftteams.uservoice.com/forums/555103-public/suggestions/16940467-allow-sending-messages-to-yourself
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Best regards,
Leon