I'm no Dodge/Ram fan boy (sticking to my '97 Ford PSD, ordered new, for the foreseeable future), but I can say that Ram dropping the Cummins name - even if they use effectively the same engine made by an associated FICA/Iveco/Whatever company, would be a terrible marketing move - they're heavily invested in the name, and just about anything can be forgiven because... "I just love that Cummins". Change the brand of the motor and the slightest thing goes wrong will be pinned on mismanagement dropping the Cummins, etc.
Note that Ford never trumpeted the International/Navistar engine connection; when their diesels started taking off, they had the "PowerStroke" brand, and GM similarly didn't make a big deal out of the Detroit Diesel connection, so when they came out with their Duramax brand, there wasn't a brand shift.
Also, in GM's case, they went from an anemic engine (215/440) to a much more powerful one (300/520) - what's not to like? If Ram drops the Cummins at this point, it's going to be a lateral move - don't quote me on this in 5 years haha but is there really that much more to be found in engines that'll fit in a 1ton that FICA is going to suddenly switch from that Cummins to a new game-changer?
I doubt it, and I'll bet they lose market share if they try.