Her name written in pinyin would be Peiyi without the tone markers, right? In that case, her name would not be written in hiragana, but rather in katakana. In katakana Peiyi would be written ペイー or perhaps ペイイ.
In Japanese, the characters written together like that would probably be read as "Hai" and "gi". Just my opinion, but I think Peiyi sounds better in Japanese than Haigi. It sounds cuter to me.