Yeah! Star goes well with all the genres except Infotainment and Kids as they already have established brands Nat Geo and Disney respectively. Ustav is really good for outside India.
I Don't see any rebranding of Star/ UTV is on the cards. UTV also have a brand legacy. And UTV movies are the first to go on to Hotstar in Indonesia. I know UTV have extended their library deal on Netflix in India. I'm not sure why they aren't adding those in other countries where Hotstar operates. UTV is currently operating as the Buena Vista of India with all the IPs, and distribution handling through UTV motion studios now. From 2019 itself Fox movies like Ford V Ferrari etc have been released in India by UTV instead of Fox Star Studios. There has been some organisational changes under after the merger interms of distribution etc.
Let me clear this thing a little :
In the Asia-Pacific region mainly in Mainland China, Star had four channels in the Mandarin Language - XIng Kong, Weishi Zhongwen Tai (Star Chinese), Weishi Diangyin Tai (Star Chinese Movies), and Star Legend Movies. They had Star Movies, Star World, Star Sports, ESPN, and Channel V too in their portfolio. Later on, they rebranded Star Movies and Star World respectively to Fox Movies Premium and Fox Life. Channel V was rebranded to Fox Taiwan. ESPN and STAR Sports became Fox Sports. The Chinese channels however just ditched the Star Logo except for Xing Kong.
Disney is hell-bent on erasing every instance of FOX around the world post the acquisition of the brand. They changed the names of 20th Century Fox and Fox Searchlight Pictures. It won't be a surprise if they rebranded FOX's assets in the Asia Pacific.
Regarding UTV, Disney totally destroyed the company post its acquisition. Before Disney took majority control of this Ronnie Screwvala company, UTV had 6 channels namely Hungama TV, UTV Bindass, UTV Bindass Movies, UTV World Movies, UTV Movies, UTV Stars, and UTVi. Hungama TV was considered to be their second innings into broadcasting after Star acquired Vijay TV from them. But it was taken over by Disney and that was the beginning of UTV's downfall. They also had Movie studios UTV Motion Pictures and UTV Spotboy. After it lost Hungama TV to Disney, UTV re-entered the broadcasting space with Bindass and Bindass Movies. They then expanded with 4 more channels - UTV World Movies, UTV Movies, UTV Stars, and UTVi - a business news channel.
Although after this third comeback, things did not go smooth as UTV Had planned. UTV soon sold off UTVi to Bloomberg. Rebranded UTV Bindass Movies to UTV Action and UTV Stars as B-Play - a music channel.
But Disney put the last nail on UTV's coffin by acquiring Bindass, and removed the UTV branding from the channel. B-Play got merged into Bindass. UTV was left with just three movie channels and their Film studios. But their woes were not over as Disney soon took the controlling stake of UTV from the Screwvalas and the rest of UTV came into their ambit.
Now UTV is nothing but a sub-brand of the Disney-controlled Star Network in India. UTV exited from the film production business and closed down UTV Spotboy. In spite of having a hit film like Dangal, UTV Motion Pictures downed its shutters. UTV World Movies too closed down. UTV is now existent only in the form of two movie channels - UTV Movies and UTV Action.
So going by what Disney did with UTV in the past, the brand may soon be a piece of History in the Indian Media World. But it will never do the same with Star. Because they know that if they attempted to change Star, their prospects would be hurt.
Sorry for giving such a big lecture over here. But some things needed to be cleared and there's nothing wrong in going elaborate if needed.