Is Apple’s next big move the revolution of the small screen? Despite the company’s less-than-stellar past attempts at putting its imprint on the television, many believe 2012 is the year Apple will up its efforts to change the device with a big product launch.

If Apple does move forward with a smart television, there’s one obvious name that would be most fitting: iTV. After all, Apple has become synonymous with ‘i-‘ products, from the iPod to the iPad.

But Apple may have to settle for something other than iTV if broadcaster ITV has its way. According to The Telegraph, the company has written a letter to the Cupertino-based hardware giant warning against adopting the iTV moniker.

ITV is denying The Telegraph’s report, calling it “entirely speculative”, but it is known that ITV’s CEO brought the naming issue up with Apple when he took the helm in 2010. At the time, he reportedly “received assurances that Apple would not muscle into its territory, at least in the UK.” With Steve Jobs’ passing, The Telegraph says there’s concern that Apple’s new CEO, Tim Cook, may not honour the assurances his company provided to ITV two years ago.

True or not, companies like ITV have reason to be concerned. After all, if Apple is able to upend the market for television programming the way it upended the market for music, major players like ITV will almost certainly be impacted, some of them in a big way.

From this perspective, the name Apple gives to its long-awaited smart television offering is probably one of the least important concerns ITV should have. Interesting, as some analysts suggest, that could be solved quite easily, with Apple buying ITV entirely, killing two birds with one stone in the process.