Don't let a name fool you. Chanel West Coast is not a reference to the Paris-based luxury design house's California locations, such as its Rodeo Drive shop. It is the name of an American rapper and model, and it is yet another example of the constant battle that luxury brands face, as the owners of established and highly appealing (to customers and others trying to establish brands and products) trademarks. A little research about Chanel West Coast filled me in on the fact that Chanel is the singer's middle name because that was her "mom's favorite perfume." I also learned that she has songs entitled "Eat my cookie," "I love money" and "I don't give a f*ck." A bit of a far cry from quilted jackets and timeless elegance. This reminds me of Gucci v. Gucci Mane, the trademark lawsuit that has yet to happen.
Chanel (the brand) does not have a federally registered trademark in classes relating to music, but that doesn't mean that it lacks grounds to sue the similarly-named rapper. Trademark dilution gives the owner of a famous trademark standing to forbid others from using that mark in a way that would lessen its uniqueness. It seems like dilution could technically apply here but may not end up being a successful claim for the design house. In short, while Chanel undeniably has a famous mark by the standards of the Federal Trademark Dilution Act, I think it would be a stretch to say that the brand is being tarnished or that trademark blurring (when the power of the famous mark is weakened through its identification with dissimilar goods) is occurring, as West Coast Chanel is tiny in terms of influence and relevance in comparison to the truly iconic design house. Thus, it seems like it could be a waste of time (and money) for Chanel to bring such a claim.
If Karl Lagerfeld wanted to do anything, he could probably sue the rapper (pictured below) for misappropriating his likeness in latest her music video (her most recent song is called Karl and she dresses up like Lagerfeld in the music video), but even that is likely more trouble than its worth. Considering I doubt that the vast majority of recurring Chanel customers even know who the like-named rapper is.