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In the police station, they say that Simon Phoenix was frozen before the chips were implanted in all citizens.
So how can he get fines for vulgarity in the museum?
How the machine can know who to fine?
(The machine doesn't say his name (unlike for John Spartan who is explicitly named), so maybe it produce a generic fine and hopes that Simon will take and pay the fine voluntarily like a good citizen?)
You've got it exactly.
The people of the San Andreas were extremely law-abiding. Anything that went against social norms was abominable, as you can see from the reactions of everyone the first time John swears near them.
As you can also see when the police first attempt to apprehend Simon Phoenix, the generally law-abiding citizens of San Andreas will comply with any direction a recognized authority figure gives them. This is evidenced by the fact that the police officers sent to apprehend Phoenix act as if a suspect not complying is completely alien to their experiences. They even require computerized assistance to advise them on the proper techniques for approaching and handling a non-compliant suspect. Even their training programs are designed with the highest level of resistance anticipated being saying "No".
In a society where the populace is so obedient and compliant, the 'honor system' is likely effective.
The machine does not say Phoenix's name, as you pointed out, because it cannot read his identification chip. No doubt there are materials capable of interfering or situations where a person's chip is unreadable at range, and it is likely that the politeness enforcement machines/toilet paper dispensers were designed to failover to a default 'citizen' when a name was unable to be read, possibly then assigning the tickets who whomever took the paper receipt (assuming their chip could be read at that point). If not, I'm sure the recipient could take their receipt somewhere to pay it.
