If Unit tests are covering all the functionality of your loosely couple software and e2e tests are covering all common scenarios followed by your users, I would name the medium tests "intangible tests". They are useful as ad-hoc tests that aim at getting a proof of concept (POC) out of the door. However maintaining them, relying on them for application quality and delaying your delivery because of them will be nothing more than paying a big opportunity cost.
- Small Tests: "Local Memory" Tests. Hopefully your current Unit tests.
- Medium Tests: "Local Host" Tests. Hopefully you don't maintain them.
- Large Tests: "Any Host" Tests. Hopefully your current e2e tests.