The two are often affectionately called: あっちゃん(A-chan, pronounced Ah-chan with a hiccup between Ah and chan) and しんごくん(Shingo-kun).
The name Oriental Radio was thought up by A-chan. He wanted a name that (1) yielded no results when searched on the Internet; and (2) had the sound 'r' (or 'l') because according to his father, the sound 'r' gives a sense of luxury and quality (as in Lexus, Corolla, and Rolls-Royce). 'Oriental Radio' has three r-like sounds (オリエンタルラジオ=Orientaru Radio).
It seems safe to say that his thoughtfulness has paid off, as evidenced by the 1,990,000 results that come up when you google 'オリエンタルラジオ.' From 0 to close to 2 million in 6 years, that's quite impressive.