you can use ingress nginx controller on kubernetes and set head and also transer to backend and manage services connection from ingress objects.

here sharing link for rewrite target from header.

https://kubernetes.github.io/ingress-nginx/examples/rewrite/

ingress nginx will be also good with ssl cert manager you can add it.

manage other thing using annotations of ingress.

check this out for ingress SSl setup you can modify it and per your need

https://www.digitalocean.com/community/tutorials/how-to-set-up-an-nginx-ingress-with-cert-manager-on-digitalocean-kubernetes

ingress will be like at last

apiVersion: extensions/v1beta1
kind: Ingress
metadata:
  name: ingress
  annotations:
    kubernetes.io/ingress.class: nginx
    nginx.ingress.kubernetes.io/rewrite-target: /
spec:
  tls:
  - hosts:
    - myapp.abc.com
    secretName: ingress-tls
  rules:
  - host: myapp.abc.com
    http:
      paths:
      - path: /my-service
        backend:
          serviceName: my-backend
          servicePort: 80

This can be done using this annotation: nginx.ingress.kubernetes.io/upstream-vhost: host.example.com

I'm not sure whether you can find appropriate annotation within NGINX Ingress Controller for Host header modification to match your requirement as well. However, you can consider using nginx.ingress.kubernetes.io/configuration-snippet annotation in order to append configuration snippet to the location block inside nginx.conf of the particular Nginx controller pod:

apiVersion: extensions/v1beta1
kind: Ingress
metadata:
  annotations:
    kubernetes.io/ingress.class: nginx
    nginx.ingress.kubernetes.io/configuration-snippet: |
      proxy_set_header Host www.example-host.com;
  name: my-app
spec:
  rules:
  - host: my-app.example.com
    http:
      paths:
      - backend:
        path: /app
          serviceName: my-app
          servicePort: http

We set here Host header www.example-host.com for target URL my-app.example.com.

I want to add my finding to this question of mine.

Although my solution is not using k8s Ingress Controller, our cluster is using Istio and Istio's VirtualService supports rewrite the uri and authority (Host header) as documented in this link: https://istio.io/docs/reference/config/istio.networking.v1alpha3/#HTTPRewrite

To know how I implement that in my case, you can take a look at this link: https://github.com/istio/istio/issues/11668