Disney is going to have to keep the Fox brand alive on some level, the same way the kept Miramax and Touchstone going for a while and the same way Universal has Focus Features.
I mean, Disney might keep Fox 2000, which is well respected in the business (I work in Hollywood, but on the business back end, so I read the trades but have little to do with the production of anything, although I do have access to a lot of knowledge and information). Fox has a good reputation as a television production studio and while they haven't had the tentpole success that Buena Vista has, their library is far deeper and historically more interesting and diverse than Disney's - which is why both Comcast and Disney wanted access to it.
My big issue is that Disney will end up controlling Hulu. I would prefer that as part of the deal, Disney have to sell Fox's share 50% to Warner Media (I'm sure Warner Media would like it all but that would THEN make WM the largest - albeit not a majority owner) and the other 50% of Fox's share to Sony or Lionsgate or Paramount.
Right now, Universal and Disney 30% each, Fox owns the other 30 and Warner Brother's recently joined but only for the 10% that wasn't owned by the other three.
It would be good for consumers if Hulu exists to compete with Amazon Prime and Netflix and it would be good for consumers and the studios if Hulu is NOT owned majorly by ONE of the studios. Selling 15% (or half of Fox's share) to WM gives them 25% - or you could sell them enough to get them to 30% and sell the remainder (10%) to Sony, Paramount or Lionsgate.