One thing for sure is that Fox international channels will be rebranded as Fox brand will remain in US at least for Fox stations which carries Lucifer,Gotham etc.Else they will have pay a brand license which they will probably don't want to.
Btw Disney previously bought two channels from Fox in USA -
1.Fox Family which was rebranded to ABC family and now to Freeform.
2.Fox kids which is now Disney XD.
Just FYI, these are Disney presence in India curretly
1.Disney (Disney,Disney XD,Hundama etc) and Disney UTV (Bindass,UTV movies etc)
2.Sony ESPN (ESPN is a jont venture with Hearst 80:20)
3 With TV18/Network 18 (Histoty,FYI)- These channels Disney have JV with Hearst(50:50)