Hi bastna
If this is a permissions issue, it should throw an error 403 or Insufficient privileges to complete the operation when you click on Custom domain names under azure AD.
Still i would suggest to check your permissions. Make sure that your Global Administrator account has the necessary permissions to manage custom domain names. You can check this by going to the Azure AD directory in the Azure portal, selecting "Users and groups", and then selecting your Global Administrator account. Under "Directory role", make sure that the "Global administrator" role is selected.
Also check the Azure AD tenant: Make sure that the Azure AD tenant is healthy and functioning properly.
If not, I would recommend opening a support ticket with azure AD technical support with the requested traces from the browser while you repro the issue.
Details here - https://learn.microsoft.com/en-us/azure/azure-web-pubsub/howto-troubleshoot-network-trace#collect-a-network-trace-in-the-browser-browser-based-apps-only
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