Customizing the Containers’ URLs – PB Docs 2022

When creating a Container Instance, you can specify a DNS
name-label value that customizes part of the URL Azure exposes for you
for accessing the container (the Fully-Qualified Domain Name or FQDN
field in the Container Instance’s Overview Page). Unfortunately, there’s
no native way of specifying a custom domain name for a container
instance.

However, there are two approaches to this limitation: