I've seen it go both ways.
For things like laptops, it's very easy as you can google the part number or go to a laptop LCD site and put in the model number.
Many laptops have a standard type of connector so you have to match connector, resolution, size, connector location and whether or not it uses CCFL or LED.
Resolution can be an issue because most laptops over 1366x768 have a different cable than ones that are 1366x768 or lower because it required both channels.
Other devices I've had a harder time with if they aren't common things like portable video games. We had a timeclock at work that had a cracked screen and I googled every number on the LCD module and found absolutely nothing. When I contacted the vendor, they would not give me a part number, just said for us to send it in for refurbishing.