How do I define the name of image built with docker-compose

For docker-compose version 2 file format, you can build and tag an image for one service and then use that same built image for another service.

For my case, I want to set up an elasticsearch cluster with 2 nodes, they both need to use the same image, but configured to run differently. I also want to build my own custom elasticsearch image from my own Dockerfile. So this is what I did (docker-compose.yml):

version: '2'

services:
  es-master:
    build: ./elasticsearch
    image: porter/elasticsearch
    ports:
      - "9200:9200"
    container_name: es_master

  es-node:
    image: porter/elasticsearch
    depends_on:
      - es-master
    ports:
      - "9200"
    command: elasticsearch --discovery.zen.ping.unicast.hosts=es_master

You can see that in the first service definition es-master, I use the build option to build an image from the Dockerfile in ./elasticsearch. I tag the image with the name porter/elasticsearch with the image option.
Then, I reference this built image in the es-node service definition with the image option, and also use a depends_on to make sure the other container es-master is built and run first.