When creating a container using the docker run command the --name option can be used to give the container a specific name.

docker run --name my-container my-image:latest

Of if the container already exists the docker update command can be used.

sudo docker update --name my-container <container ID>

You can use the docker inspect command to view the JSON for the container.

~]$ sudo docker inspect my-container | jq .[].Name
"/my-container"

The docker container ls or docker ps -a command can then be used to display the container. Notice the name of the container is foo.

~]# docker container ls
CONTAINER ID   IMAGE       COMMAND                 CREATED        STATUS   PORTS  NAMES
d937372c09ab9  foo:latest  "/docker-entrypoin..."  6 minutes ago  Created         foo