I also add my baby boy's English name on his ID & passport.
I suggest you to be consistent in all her document. Since for myself, in my HK ID, i have added English name, but for my Aust passport, I did not .... there is a bit of trouble sometimes.
我個囝囝出世紙只落左英文名無落中文名譯音架。同埋出生登記處無要求我一定要落中文名譯音喎。如果將來去外國讀書做嘢,有個中文名譯音仲麻煩,D洋人鍾意當你中文名中間個字就係你個名,例如証件寫你叫Chan Tai Ming Michael,咁D洋人就係咁叫你做Tai,我之前在澳洲住左七年,所以我知道,你要成日同人講你prefer人地叫你個英文名。