There is no serial number on the individual die, but TSMC has very unique test lines on the chip that would easily identify if it was in fact made at TSMC.
Due to the way lithography works, it isn't easy to make each die different. The usual way to put serial numbers into chips is with efuses, but not all chips have any efuses at all, and it would require collaboration with the customer to design a way that they be programmed and read (probably on a JTAG chain).
Either one time fuses and some software, or via directed beam energy fusible or breakable links.
Edit, yeah like the other comment suggested.