Point custom Domain to the google cloud function through global https loadbalancer with serverless NEG as backend

Question

I had a running myfunctionname cloud function with HTTP trigger URL:

For Ex- https://us-central1-my-project.cloudfunctions.net/myfunctionname

Now I want to map this cloud function URL to public domain URL

For Ex- https://my-domain.com/path

Public domain URL is setup in DNS to point to loadbalancer. Global external https loadbalancer is created with host, path rules & backend service

Host: my-domain.com , Path Rule: /path , Backend Service: Serverless NEG pointing to myfunctionname cloud function

Now if I hit the API endpoint with the Cloud Function Http trigger URL, API response is 200 OK, it's working

GET Request on endpoint https://us-central1-my-project.cloudfunctions.net/myfunctionname/show/jobs

But when I hit the API endpoint with the custom domain URL:

GET Request on endpoint https://my-domain.com/path/show/jobs

API error response is 404 Not Found. Cannot GET /myfunctionnameshow/jobs

Can someone please point out the issue why my custom domain URL is not redirected to cloud function URL? Actually my expectation is hitting https://my-domain.com/path/show/jobs API endpoint should be equivalent to hitting https://us-central1-my-project.cloudfunctions.net/myfunctionname/show/jobs API endpoint.