You have two option to share the domain name.
First host both sites with a virtual machine you can configure to host multiple web sites. Say a windows machine with IIS.
Second is to use a loaded balancer with proxy support, like ngnix.
You are probably better off using two domain names with common subdomain. Azure supports custom domain names. See
https://learn.microsoft.com/en-us/azure/app-service/manage-custom-dns-buy-domain