HELP! Baby born to UK parents in Taiwan (passport question)

We are one british and one taiwanese parent. At the hospital we requested an english language birth certificate and put the ‘proper’ english name, not a pinyin version. If I remember well there’s a thread somewhere that basically says if you don’t have an english birth certificate it is a lot more diffcult/impossible.

When we went to get all our other documents we could use the english birth certificate to show the correct english name.