I guarantee you won't last long if you start a Coca-Cola School of Hairdressing, even though the beverage company doesn't compete for that business.
Feel free to start Kik Paper Co, however.
And keep in mind that the OP I was responding to was arguing that if the name is unique it gets extra protection. That's false. Fame offers extra protection, uniqueness does not.
Are you sure a court wouldn't consider that qualifying as a famous mark? I'm not going to dig into case law, but my guess is it very well could be.
"Evidence relevant to the fame of a trademark may include sales, advertising and revenue figures; geographical scope of use; channels of trade; registrations in home and other countries; past enforcement efforts; and the results of consumer recognition surveys (provided the survey methods are approved by the courts in that jurisdiction)." http://www.inta.org/TrademarkBasics/FactSheets/Pages/FamousW...
Teenagers represent 9.5% of the US population meaning that 3.8% of the US population (using their 40% figure) have "used" their app. Alternatively the 240 million registered users would imply about 3.5% of the total global population has used it.
I can say that I honestly have ZERO doubt that "kik" would never be ruled famous by any possible measure.
To be even reasonably certain in this case, I would need case law of similarly well-known brands being challenged. Do you have some? Capturing 40% of their target market seems pretty well known to me, but again, that's meaningless without the case law.
Mcdonald's was able to show that there would be consumer confusion DESPITE Mcdonald's not doing hotels nor Mcsleep inns not doing food.
As a result, Mcdonalds basically has an open trademark enforcement on "Mc-" whatever.
While I'm not fond of the judgement here, it was nonetheless decided thusly, and contradicts your otherwise accurate (so far as I know) statement. (And to weaken my own point, I believe Apple lost a similar case about i<whatever>, so nothing here is clear and reliable.)