> I understand that the model name might appear in prompts for distillation (I guess? "You are RipOffModelv2, learn from these responses from Claude")

This does not make sense. You wouldn't send such a prompt to the Claude model. And when you're sending the prompt (anywhere) you don't have the response yet. This is not how distillation works.

There are a lot of companies reselling Claude to Chinese users. You use their base URL but it's still going to Anthropic.