Yes. This is officially acknowledged (at least in the german CovPass app) and is a feature. You are able to "manage" multiple passes in said app. This is intended for accessibility (elderly partners with a shared smartphone, legal guardians for people with disabilities).

And yes, in theory at least the name should be crosschecked with a form of ID. It's just a digital copy of a legal document, you could easily borrow or copy the paper version from someone else as well.