Hello Matt,
Is Web.BaseUrl set to https://host.name.net in https://host.name.net/administration/advanced-settings? Is there a reverse proxy between ProGet and the internet that requires authentication, or that might be modifying authentication headers?
If you access the /v2/ URL in your browser, there should be a header like WWW-Authenticate: Bearer realm="https://host.name.net/v2/_auth",service="host.name.net".
EDIT: We have updated our Docker documentation to include this information and more information about setting up your Docker client and ProGet server.