Authentication Required error when pushing image to private trusted registry

When I tag and attempt to upload my docker image to a private registry, I get the following error message:

root@localhost: docker push mydomain.com/orgname/project-name/project:latest
4121acbcce4d: Preparing
84b2243fb072: Preparing
65f4bdf80254: Waiting
5275557908a9: Waiting
62994e70aaac: Waiting
775a459cc2f9: Waiting
a094d99c0e45: Waiting
cacbcad1064d: Waiting
c86bc51a03ca: Waiting
80716a2ba414: Waiting
unauthorized: authentication required

The odd thing is that I can log into the registry server without issue, and I can push to my own project repository. Any idea what’s going on?

My docker client is version 1.12.6, running on CentOS 7.4.
The server is running 17.06.2, running on RHEL 7.4.