How can you identify the chipset of a usb device in Linux?

There is no general way to determine the chipset unless the manufacturer changes the ProductID for each different chipset, or updates the revision number. And even then you would need to know how the ProductID maps to the chipset.

Did you try

lsusb -v

When the verbose switch is used lsusb prints a lot of information.

The closest you can get to learning about the product without opening the casing is the VID (Vendor ID) and PID (Product ID).

But AFAIK, many vendors use same VID and PID (for driver compatibility) and change the chipset.

You can open the case and hope the manufacturer did not erase the part number.