if I have 10 custom domains within an app, do I need to add the “asuid” entry 10 times?

If you have multiple custom domains linked to the same Azure App Service, you need to create a separate asuid TXT record for each domain to verify them.

• Please refer this MSdoc 1 and 2 for better understanding about DNS TXT record asuid.
• To verify ownership of each custom domain, you need to create separate TXT records. If you have multiple custom domains (like domain1.com and domain2.com) for the same App Service, you'll need to set up individual asuid.<subdomain> TXT records for each one, each with its own unique verification ID provided by Azure.
• Check this blog for more detailed information about custom domains.