Similarly, although people do this less now, Beijing is not pronounced Bay-zhing, but rather Bay-Jing. There is no "zh" sound (the s in 'measure') in Chinese, despite all the zh's and x's you see in Pinyin. There are zh's, q's, and x's because there are two j (as in juice) sounds, two sh (as in shirt) sounds, and two ch (as in cheese) sounds and they have to be differentiated somehow in Roman script.
The band "Xiu Xiu" in Chinese (because it's named after a Chinese movie) is pronounced something like shyo shyo or see-oh see-oh, but with very little emphasis on the "see" and compacted into one syllable for each Xiu. It's not Zoo Zoo. There is no "z" sound in Chinese, although there is a "dz" sound.
If you don't care about pronouncing the Chinese way, that's fine with me. But if you are trying, I'm just giving you a heads up.