Currently if you have a *.trafficmanager.net domain and point it to an azure website you get warnings from browsers saying that certificates don't match (if you make https requests).This is because .azurewebsites.net have a certificate for .azurewebsites.net but not *.trafficmanager.net.
Please refer to the feature request: https://feedback.azure.com/forums/169385-web-apps-formerly-websites/suggestions/7379755-add-the-trafficmanager-net-ssl-certificate-to-we that refers to the similar issue.
However, now you can use *.trafficmanager.net with SSL if using Azure Managed Certificates (in preview)
https://azure.microsoft.com/en-us/updates/secure-your-custom-domains-at-no-cost-with-app-service-managed-certificates-preview/
It is not available out-of-the-box (even so SSL for TM in WebApp has green checkbox already) - however can be easily achieved using small PS snippet - see following URLs for additional reference and the PS script:
https://learn.microsoft.com/answers/questions/1181/managed-certificates-behind-traffic-manager.html
https://dotnetdevlife.wordpress.com/2019/11/11/app-service-managed-certificate/
Hope this helps. Please let us know if you have any further questions and we will be glad to assist you further. Thank you!
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