With the latest release of Docker-Compose (1.18) they added the possibility to achieve exactly this - i.e. setting a global unique name for networks from a docker-compose.yml. Although it is not terribly well documented, you can read the docs for this change -> https://docs.docker.com/compose/compose-file/#name-1
You need at least Docker Engine 17.06.0 for this to work. If you have both - recent Docker Engine and a still hot docker-compose 1.18 you can achieve it with:
# you need to use the latest version of docker-compose yml
This will create the global net
my-network-name. Seems like setting the same global network from different docker-compose.yml does not have any effects (nor an error is displayed); although I presume that then all services will obviously in the same overlay network.
docker-compose down will try to remove the global network.