When you use docker run -e POSTGRES_PASSWORD=password -d postgres, the POSTGRES_PASSWORD would be set for user postgres as default. you can specify your user with POSTGRES_USER environment.
Second thing is that when you run a postgresql container and don't bind any ports for that, you can't connect to that container from outside. So you won't being able to connect to your container with pure pqsl command. Here you have 3 way to connect to your container:
1- Use docker run -e POSTGRES_PASSWORD=password -p 5432:5432 -d postgres to run container, then connect to it with psql -h <YOUR_IP> -p 5432 -U <USERNAME>
2- Get your container ip with docker inspect <CONTAINER_NAME> command, then connect to it with psql -h <CONTAINER_IP> -U <USERNAME>
3- Use psql inside your container with docker exec -it <CONTAINER_NAME> psql -U <USERNAME>