Disney will own the company and for the sake of taking advantage of brand name recognition, it's my bet 'ALIEN' and 'PREDATOR' movies will still be released by Fox.
It makes no sense to release 'ALIEN' or 'PREDATOR' movies under the Disney banner and as they own Fox now (as of 20th, March), there's no point in releasing future movies under a different studio name, either. They own the studio, 'lock, stock and barrel.'
Once the settlement is made and the handshake is done, there will be some staff shake ups and it will be business as usual for Fox, but the profits will go in a different direction than they have for the past decades.
On the surface, nothing will have changed. Fox is a world recognised brand name. Disney will want to capitalise on that. They will instill changes but ultimately what it boils down to is business for the old company under new ownership. Fox won't cease to exist and will still make movies in the future, most likely releasing new titles under existing IP's to bolster public confidence once again.
Outwardly, to us, there will be no visible change. It will be the shareholders that have changed completely, but the institution itself will continue to exist - with changes - but it will still push out product the public is familiar with.
How that quality will change, is anyone's guess right now.