Remove project name parameters from pipeline templates

This PR (https://github.com/dotnet/docker-tools/pull/884) introduce a template pattern where `internalProjectName` and `publicProjectName` parameters were defined and passed around to templates rather than hardcoding the actual AzDO project names:

https://github.com/dotnet/docker-tools/blob/86df1f66c815ed8bc35c50147228d003aadcd9b7/eng/common/templates/stages/build-test-publish-repo.yml#L22-L23

This pattern doesn't provide much value. In fact, it has negative value because developers need to ensure that these values get passed around through the template graph. Omitting this can lead to unintended behavior. We should consider removing these parameters and simply hardcoding the project names where they are needed.