Unfortunately there is no surefire way of identifying the wood trim. I requested my trim details from Jaguar based on the VIN, and that information did not include anything about the veneer.
Well, when I say "surefire", I mean especially the stain. The wood pattern can be identified (for example bird's eye maple is very easy), but it's difficult to find an exact match because there appear to be differences in even similar-looking pieces and photos often lie (camera settings, where it was taken, daylight/clouded over, whether it was edited in any way, what kind of display you view the photo on, etc...).
I bought an ashtray cover and gear surround for my manual car from eBay, as they seemed to be the same exact colour as the rest of the trim in my car. However, you can see here that they are significantly paler and lighter than the rest of the trim:
Hunting for that steering wheel was a nightmare, I asked the seller to take photos in different conditions with different cameras and then editing them myself (changing white balance settings) to try and make sure the colour is correct. I ended up buying a steering wheel with the correct wood but black leather (my interior is dove/granite), and had to have it re-trimmed at a car interior workshop.