I thought it would be funny to translate their name in both ways (meaning and phonetic). So you can easily get what it's kun'yomi and what's on'yomi. (Kanji, Mandarin, Meaning, Japanese)
高橋 愛, GaoQiao Ai, 'high bridge' love, TAKAHASHI AI
新垣 里沙, XinYuan LiSha, 'new wall' 'inner sand', NIIGAKI RISA
龜井 繪里, GuiJing HuiLi, 'Turtle fountain' 'painting inner', KAMEI ERI
道重 沙由美*, DaoZhong "Shayoumei*", 'Way Heavy' "sand inner beautiful*", MICHISHIGE SAYUMI
田中 麗奈, TianZhong LiNa, 'farmfield middle' 'beauty enduring', TANAKA REINA
久住 小春, JiuZhu XiaoChun, 'long stopping' 'little spring', KUSUMI KOHARU
光井 愛佳, GuanJing AiJia, 'shining fountain' 'love fine', MITSUI AIKA
純 純, Chun Chun, Pure Pure
琳 琳, Lin Lin, piece of Jade x2
*) Sayu hasn't got kanji name. Translation from さゆみ into 沙由美
Actually, a few others and myself have translated some of their chinese names into pinyin over at mm-bbs. So if you want you can check it out there.
Why don't the Taiwan website just used the name "Sayumi" ? They can have all the words in Chinese and then their names in alphabet.
It wouldn't really help, I guess. Cause the main language used in Taiwan is Chinese, thus most stuff has been translated into Chinese.
Also, because Sayumi's name isn't in Kanji, they tried to reproduce their names phonetically in Chinese instead. However, for some others like Yoshizawa Hitomi whose name is written in Hiragana, they used the available Kanji for it (note that Melon Kinenbi's Saitou Hitomi's name is written in Kanji).
So I'm guessing that they'd use anything that is available to them, to switch into Chinese.