Having too good a brand is a problem.
Lets all shed a tear for Google. In danger of losing control of its brand due to people speaking of "googling" things, they've gone on the attack over people using the brand as a verb.
So, can you end up having too good a brand? Read more.
Back in the 70's, Xerox totally freaked out when they became a verb meaning to copy a document. Once having the lock on all copy/print sectors, Xerox now holds 28% of the copier market.
I think I heard Google first used as a common verb back in 1998 or 1999. Google variant words have also become commonplace - there are even websites. For example, Googleism.com is a popular website thats been around for years (try checking on "jolitz" - and who says I'm hard to work with?).
During all of this, the brand manager is loving the attention as the brand becomes embraced by mass culture, no longer just a obscure techno item.
But, like to much ice cream, loss of brand is a very real thing. Say a website names itself "google-me.com", and in court shows dozens of press articles from major outlets where its fallen into common use. Sorry Google, google-me now is its own, separate thing. And sorry, you can't control it.
Imagine what it would be like, to have a multibillion brand, and then not be able to control what it means.