Some interesting points and theories here. My view;
1) Quantum was blown in the film that bears its name in its title. The opera house scene, and then whatever Dominic Greene told Bond before being lost in the desert. The deleted scene intended for the end, in which Mr White tries to assassinate Guy Haines, suggests he was covering his tracks by getting rid of the high level members who panicked when Bond spoiled their night at the opera.
2) SPECTRE emerges out of the wreckage of Quantum, or might have been controlling it in the shadows all along. In the book Thunderball we are told that Blofeld formed a number of "syndicates" with fancy names before founding SPECTRE. Something similar could have happened here, but on a much bigger scale. And in the real world of legitimate business it's not unknown for companies to change names. With knowledge of "Quantum" now in the private domain of the intelligence sector, wouldn't make sense to wind it up and regroup?
3) For reasons already mentioned above, I doubt that Mr White is really Hannes Oberhauser, unless he had radically changed his appearance. And even then there are , to use a word from CR 2006, "tells" - giveaways that people have difficulty hiding. In the book OHMSS, Blofeld had changed radically, save in one respect, something he could do nothing about except use contact lenses. I might be proved wrong - lets not forget that SPECTRE wouldn't feature at all had the rights to it not been settled, and White's fate should have been death at the end of QoS, so some kind of backstory about him could be cobbled together for the film Spectre. But I have my doubts. He's fallen foul of SPECTRE, I think, and the next character;
4) Franz Oberhauser. Either he really is Oberhauser junior and in one of those incredible co-incidences Bond is pitted against someone he knew, temporarily, in his early teens. Or Oberhauser Jnr. really was Ernst Blofeld under another name in his youth and Bond didn't know - why should he? (And the book Thunderball provides precedents for Blofeld changing his name and appearance before deciding to return to his birth name.) Maybe at some point in the new film Oberhauser's "real identity" is revealed one way or another. Or;
5) "Oberhauser" has been doing his homework about Bond. This British agent who has cost Quantum/SPECTRE "time, money and effort", as Dr No once said, might be the target of a very personal revenge by Blofeld, with the latter adopting the name Oberhauser, changing his appearance to match, and using what he's learnt about Bond to try and undermine him and MI6. It sounds bizarre I know, but is it as bizarre as any other theories about Oberhauser=Blofeld?
6) Oberhauser isn't Blofeld - someone else is. That is a possibility - inverting the screen treatment idea from the 1970s for TSWLM about a "coup" within SPECTRE. Oberhauser is defeated in Spectre but the organisation endures and someone else takes over and that someone is ESB, who we don't see until the next movie. But it is a bit clunky and repetitive, I think - Quantum is blown, re-emerges/is taken over by SPECTRE, which in turn is defeated and its leader Oberhauser is captured or killed, only for SPECTRE 2.0 to appear in the next film with "you know who" finally in charge.
7) Andrew Scott's character is really ESB? It's an interesting idea - Bond out in the field causing havoc while the real "Number One" is at home in the back office quietly causing trouble - and running SPECTRE? - from the heart of British Intelligence. Again it would fit the description of "Blofeld;The Early Years" in the book Thunderball as the back office boy making a few bob on the side by trading secrets. But that was in ESB's early days. We're considering here someone at the highest level of British intelligence running a global crime syndicate. Isn't there a risk of being found out? Then again there are real life precedents of British intelligence chiefs working for the opposition. Interesting, but I have my doubts.
