Carrington is relatively new though isnt it. The training ground used to be at The Cliff when i was younger. Old Trafford isnt comparable to Carrington. If we're asking a serious question regarding would manchester united fans accept a renamed stadium then no, obviously. Of course what we could actually do about it is another question...
Carrington (THE AON TRAINING COMPLEX) is 16 years old, it opened the year after the Treble was won.
It's the human equivalent of a hipster child with an iPhone, it's new in terms of a building but 16 years is still a long time. Architecturally new? maybe.
Old Trafford is an iconic stadium, and place in sport. It's 106 years old, It's the 4th Oldest sporting arena in the world (Anfield is older in English Football).
It'd still be known as Old Trafford by people, and the Theatre of Dreams.
So it's essentially a protected monument but it doesn't mean the naming rights couldn't be sold.
A companies name could be the Suffix of the title, such as BT Old Trafford Arena, Virgin Old Trafford Arena. Contracts can stipulate the naming of it.
Virgin Theatre of Dreams, BT Theatre of Dreams. Shirts have sponsors, Players have Sponsors, things do more forward in Football.
The stadium wouldn't change as a result. As a business you should always look to increase revenue streams so I don't personally see harm in it.