But wouldn't Tang Yi originally have had the name of his grotty adoptive father, who abused him?
If Tang Yi had his name, then yes, that's a good reason for Tang Yi to take "Tang" instead of whatever he had previously.

Would that not be a good reason for TGD to be happy for TY to take his name even if he knew whose son TY really was?
I think knowing vs not knowing is the key. It's really awful for TGD to give TY the surname of "Tang" if he knew whose son he really was.

(Plus it was Tang Yi's choice, since ZHY doesn't change her name.)
I mean, yes, it is Tang Yi's choice, but also...traditionally, no. Children take their father's names. Wives do not. There's a huge difference.

So yeah, even given that, if TGD knew whose child TY was, it would be perceived as a horrible thing to do to cut him off entirely from his true bloodline.

And if he did know, maybe the prospect of explaining the whole parentage saga to TY was just too complicated and fraught with danger to TY's stability & happiness, and to LLZ, and potentially the syndicate. Better a fresh start?
This is a plausible reason, particularly if there was LLZ's influence, and she was pretty intent on cutting off CWH's access to his son, by lying to him about the abortion.

Ah, the forever mystery about this show.