I remember when Claude identified as ChatGPT a long time ago. It proves nothing else than that there is a lot of training material on the internet with Claude as the AI.
I don't understand why labs don't include correct model name in the training process. Almost nobody seems to be willing to tell their models who they actually are.
If the model works correctly, you don't need to include the model name in the training process. You just add in the system prompt "You are X, trained by Y" and the model will claim to be that. That also allows users to "white-label" the outputs sort to say.
This approach is basically how all "models know who they are" (they don't actually typically "know" that at all), it's just a system prompt instruction in the platform you use.
That only makes sense if you don't sell access to the model for 3rd party product development. One of those products is chat personas/agents. The company integrating the model will want it's own identity.
You can put anything in the prompt. And if you have bare model that you don't give any prompt from the start and want to find out which model you are talking to, you are out of luck.
I think Qwen teaches its models that they are Qwen. Most others don't bother.
Because they do not know the name of the model before they train it. There is also distillation, where multiple models will be trained from a larger one. E.G. Sonnet was promoted to Opus at one point after it surpassed expectations.