Multiple Microservices in CI environment
So if we change it for one service, we need to update it in each docker-compose.yml in each project.


That's sounds like duplicate code and there are many ways to avoid that. But without more detailed information about how your setup looks like it's difficult to help. 

Within a pipeline you can access other projects and their source code. Maybe Git Submodules is an option. Or you might be interested in the include keyword of GitLab CI.