Can mainland residents still use their original identity cards after becoming Hong Kong residents? The names of ID cards and Hong Kong ID cards are different?

Theoretically, it is legal, because if mainlanders immigrate to Hong Kong, they will normally cancel their original mainland household registration. In Chinese mainland, the Hong Kong and Macao Pass can be used as an ID card. As for the different names above, do you mean the difference between traditional Chinese characters and simplified Chinese characters? It doesn't matter if it's just a simple difference. If he changes his name after immigrating to Hong Kong, he needs to show relevant certificates, but you'd better advise him to open a bank account with the Hong Kong and Macao Pass (actually called Home Visit Permit) if possible.