Arriving a little late to this party, but for more than 30 years our Kwan Jang Nim had "Korean Karate" hanging outside his doors. Only recently did he change it to S.H. Kang's Tae Kwon Do. In my particular case, it fits, since we practice adaptations of Karate Kata (Kicho Hyungs, Pyung Ahn Hyungs, Bassai, Naihanchi, Jin Do, Kang Son Kun, etc.) I personally don't see a problem with the nomenclature.
The modern TKD curriculum has little resemblance to classical Karate Do, so I can see how it could be misleading in that sense. However, there could be an argument that modern Karate has little resemblance to classical Karate Do.. .
As ol' Billy Shakespeare said: ".. .a rose by any other name, would still smell as sweet.. ."