What's the etymology and significance of yuenyeung (鴛鴦)?
鴛鴦 is actually the name of a bird; more specifically, the mandarin duck. 

Here's an image:  


(Look at how cute they are!)  

In Chinese culture, the mandarin duck is a symbol of lovers, much like the lovebird in English culture. The term 鸳鸯 is often used to describe pairs of things that make a good match. As for your drink, this most likely refers to the tea and coffee, which, despite tasting very different (much like the colour difference between the male and female duck), are actually perfect for each other.

The common radical, 鳥, means "bird". "鴛" refers to the male duck, and "鴦" refers to the female.