Today's free Metro newspaper had an article about US band One Direction complaining about British boy band One Direction. A lawsuit has been filed. The British group are in Simon Cowell's Syco label.
The US band formed in 2009 and are quoted as saying that they were the "first to file a patent and trademark application."
You can't patent a name or wording (a common error), but you can certainly register trade marks. In February 2011 the trade mark "One Direction" was filed for as a US trade mark, which is awaiting registration, for "Entertainment, namely, live performances by a musical band". Oddly, despite the claim to formation in 2009, it states that its first use in commerce was on the 2 October 2010.
There is also Bandname.com™ , a free registration site even if you only want to search for band names (why make life hard for bands ?) where new bands can list unique names to avoid possible conflict, although I am not sure of its legal standing.
The US group is asking for the British group to change their name and for one million dollars, as the British group has been successful in a US tour. According to an InsideCounsel page, the lawsuit is based on trade mark infringement -- which is strange, as the US application for a trade mark is still awaiting registration.
[The IPKat blog has a very useful post which shows that the British group have applied for a US trade mark. Ed., 17 April]