I'd go with a brand name rather than something that's trying to describe the ticket properly in one word. "Value Single" works reasonably well, or even "Saver Single" (yes, it's different from what that was, but DB used to have a walk up fare called a Sparpreis and now it's a quota controlled advance type fare). OK some of them aren't, but they are cheaper than Anytimes so it's not entirely silly.
The break of journey restriction should be removed on Advances. It is nonsensical to prevent people leaving stations mid-journey where the booked trains have a long enough gap to be worth popping to the shop, and just creates pointless arguments and fun for deliberately awkward staff. And if these are available on all journeys on relevant trains, as they would be, there's no reason to prevent starting/stopping short. Break of journey (i.e. leaving the station for any purpose) should, provided booked trains are used, be permitted on all fares. And if one wants to insert an hour's extended change to pop for lunch or similar, one should be allowed to do so at the time of booking without splitting tickets.