I have a requirement to have different APIs in single API Management service which are dependent on incoming HTTP host. Example
*.company.com -> API 1
*.anothercompany.com -> API 2
Something very similar how Application Gateways handles this situation where you can have listener for each custom hostname and route it based on which listener received incoming request. I can see that API management service can responds to multiple custom domains but I don't see any option to tie incoming request to specific API
Not directly possible at the moment. If you have any network appliance in front of APIM you could consider doing URL rewrite at that level. Otherwise, one workaround is to use send-request policy to invoke an operation on APIM itself via 127.0.0.1 localhost IP: https://learn.microsoft.com/en-us/azure/api-management/send-request-policy#usage-notes