Here's California's statute on the matter, search for "17052": http://law.justia.com/codes/california/2009/corp/17050-17062.html In a nutshell, it has to either contain the words "limited liability company" or end in "LLC" or "L.L.C.", cannot be a name that's likely to mislead the public, cannot be the same as another LLC or corporation, and cannot use the words "bank," "trust," "corporation," "incorporated", etc...
There are probably some practical limitations imposed by the Secretary of States' office -- they probably wouldn't allow you to use an "unpronounceable symbol" a la the artist formerly known as "Prince," for example.
Usually, it's best either to form the LLC, or at least to reserve the name, before spending much money or effort in reliance on that name.
The problem with names is that it's hard to get a ".com" address for it usually. So while you can pretty much name your company legally using any name (that is not already taken by a large brand, don't call your company "Apple, Inc." obviously), whay website will your business card show?
No one cares about your legal name otherwise.