https://www.npr.org/sections/health-shots/2019/05/07/7207022...
Hospitals that accept medicare do have a legal obligation to stabilize patients. But we're talking 'stabilize' as in 'you're not dying'. If you're alert and capable enough to be arguing with people and you're not a psych danger, you're likely stable enough to legally be thrown out on the street.
The discussion here is whether there is a legal obligation to identify yourself. If there is such a requirement, it would apply to someone who is fully capacitated but refusing to identify themselves. It would not apply to someone who is unable to identify themselves due to incapacity, because such a person obviously lacks any criminal intent.
If there's no risk of criminal exposure, even insured people should start doing this. Hitting hospitals with uncompensated care under EMTALA is one of the few points of leverage we have to fight back against these murderers. Hospitals are, by and large, not innocent parties in this -- several hospital groups are even members of the Partnership for America's Health Care Future terrorist group, which bribes politicians to fight Medicare for All.
It would bring me great pleasure to get to tell a hospital to go fuck themselves and to quit bribing politicians to fight M4A if they want to get paid next time.
Giving a fake name is fraud, and people have been arrested for doing that at the ER. (Fuck America.) But I don't know that there's any legal obligation to give any name at all. If you don't give them a name, you're not lying to them, and oops, looks like they don't have a way to bill you. As you note, hospitals are legally required to provide emergency stabilization without regard to ability to pay.
I suppose the hospital could try to call the police, but AFAIK the police cannot compel you to identify yourself without reasonable suspicion that you have committed a crime.