@Michael Dunkel , Based on my understanding of your questions description,
The *.azurewebsites.net
domain name and the certificate is provided and owned by Azure.
I understand the requirement of removing the default domain, but there is no way disable it. You could instead accomplish this by adding a rewrite rule
(Or Redirect rule).
A rule to detect if the user has accessed the website using the Azure default domain and issue a HTTP 301 or 403.
Just to highlight, by default, http://yourdomain.azurewebsites.net works even with custom domain added, and the site admins aware about the URL can access, but typically end users would not access this URL directly (unless explicitly shared).
Reference on other approaches outlined in the similar discussion threads:
- can-we-remove-disable-http-domain-azurewebsites-ne
- prevent-azure-default-domains-being-indexed-search-engines-anton-pham
- How to make sure that google doesn't index you Azure subdomain? - You may try adding a robot.txt file for Google indexing the site as mentioned by Peter on SO discussion thread.
I'd posted an answer on similar discussion thread:
- azurewebsites.net domain indexed in google
- can we remove/disable http://domain.azurewebsites.net domain after adding custom domain?
More info:
App Service *.azurewebsites.net TLS Cert Renewal for Web Apps, Functions, and Logic Apps (Standard)
Kindly let us know if my understanding is correct, or please share more details about your scenario/requirement.
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