I've found and old Arduino Nano in my stuff and when i checked it noticed there is no logo or brand on its serial-USB communication chip. i connected it to my PC but it wasn't recognized. so i installed CH340G/341 driver but no good came out and my PC can't recognize it. has anyone had such a problem before? what kind of driver works for it? i attached a photo of its serial-USB communication chip, so take a look at if you don't mind. it would be a great help.
If Windows, go to Device Manager, and open either Ports or USB, wherever the unknown device is located. Right click, pick Properties. Go to Details tab, find Hardware IDs. You should see something like USB\VID_1234&PID_5678, maybe some other numbers. VID is the Vendor ID, PID the Product ID. Google those, like VID_1234&PID_5678, and you should see the brand and ideally the specific model in there.
The above answers by @dremu and @johnwasser should get you on the way; in lnux, lsusb and dmesg are your friends.
I have the same problem that laser-engraved chips are barely or not readible. This is just a suggestion for the photography of the chip: take photos under an angle as shown below.
By the way, the chip is more than likely the CH340; the number of pins in your photo matches the number of pins in mine. FTDI chips definitely have more pins; not sure about chips starting with PL or CP.