Chinese mainland passport cannot use traditional Chinese. Please indicate the change of pinyin when filling in the form. For SAR passports, traditional Chinese and Cantonese pinyin can be used. Remember to add "previous name" or "alias" to your passport. As for the previous certificates, as long as they are used abroad, they generally need notarization.
It is suggested to consult relevant departments according to the specific situation, such as the Exit-Entry Administration of the jurisdiction or the Exit-Entry Administration of the Hong Kong SAR Government.