There shouldn’t be a problem with the name, but my experience tells me that people don’t comprehend it the majority of the time, and assume incorrectly that cold brewed must be served cold. This mentality is even here in this thread in a few places. It does seem like some other word than “cold” might help avoid leading people into an erroneous conclusion.

Yeah I greatly enjoy cold brew too. But it's too easy for people working these stands to just take any old coffee that's cold (or even just "not hot) and call it "cold brew." Far too often people just don't know the difference and serve plain iced coffee.

If it were called something else, maybe there wouldn't be this level of confusion, or people couldn't get away with the cheap/lazy way of just serving yesterday's leftover hot coffee as "cold brew."