-It seems like the default name for 5E is DnDNext. That is what WotC is using most of the time when discussing the next edition. I can see why they want to avoid the concept of "next edition". They are hoping 5E will bring all the older editions together under one umbrella, while still allowing for new edition stuff...without calling it a new edition.
However, I don't like DnDNext as a name for the next iteration of D&D. It feels transitory. It feels like it invalidates what has come before (which is the actual opposite of what their intended goals are). It feels like "New Coke". While I don't have a much better answer, I think I would prefer something simple like "Core D&D" as the name of the next edition.
-One major thing that will help 5E is backwards compatibility. It is one thing to bring out the "feel" of other editions. Does 5E "feel" like 1E? Can you play a 4E style game? I think that can all be accomplished through nomenclature and system add-ons.
However, the real question is...Can I pick up an old adventure module and run it using 5E? I am fine with needing a specific rule system add-on (i.e., if I want to run a 4E adventure, I would need the "4E add-on"), but do I need to do a full conversion to make use of my old materials? If WotC can make 5E capable of running older material, they will find more people getting on board the concept of 5E.