There is nothing to stop ITV paying BBC Studioworks an amount of money for them to put a sign up saying ‘ITV Television Centre’. BBC Studioworks would still own and run it but they’d get a bit of extra money their main tenant. Come to think about it, it’s probably worth ITV’s while.
Stanhope Properties who actually own and operate the Television Centre development, would probably have a few ideas about that suggestion...
It will never be named the ITV Television Centre as ITV are really only based in Studios TC2 and TC3 for daytime shows under their sublet agreement with BBC Studioworks - Studio TC1 is open to any production and is provided by BBC Studioworks.
Television Centre is a neutral name and a perfect way to identify this iconic building. To smack the name ITV in front of it would be a huge slap in the face to the BBC, especially given it was their original building, so no it will never be named ITV Television Centre.