It's not possible to have an empty project name as it's used internally by docker as part of the key for container.

It's discussed in more detail here: Proposal: support for empty project names.

This can be done in with a parameter of the docker-compose call:

$> docker-compose -p THISISMYPROJECT_AND_NWK_NAME up -d

Unfortunately there is no way to persist it at the moment. (see: https://github.com/docker/compose/issues/745)

That's why I personally prefer adding a bash alias for my projects in ~/.bash_aliases (Debian based Linux) for example:

# project PROJECT shortcuts
alias dc_PROJECT_up='docker-compose -p PROJECT up -d'
alias dc_PROJECT_down='docker-compose -p PROJECT down'

# general docker compose shortcuts
alias dc='docker-compose '
alias dc_up='docker-compose up -d'
alias dc_down='docker-compose down'

So I can call dc_PROJECT_up to start my project with a project name PROJECT. The network name is PROJECT_default then.

Additionally you can setup additional networks with custom names in the docker-composer.yml like this (v. 2.1):

version: '2.1'

...

networks:
  mynwk:
    driver: bridge
    name: mynwk

 ...

You can check this with the following command:

 $> docker network ls

You should get a list of networks including yours and the default one.