haha, finding the part number on the turbo is a no go. its on a tiny blue and silver metal tab on the compressor housing. I only know this because ive seen mine off the car! i dont think you can see it when its fitted.
however. if you want to know your engine code, its printed in the data sticker in the spare wheel well, and will be a 3 letter code. its also hammered into the head. as you look at the engine bay from the front of the car, bottom left on the head is a tiny flay surface, about 15mm wide and 20mm long, the 3 letter code is hammered into this surface.
Go read your engine code, then compare it to the list of engine codes on here, or if you cant find it, post up the code and we can tell you which turbo you have.
Chances are on a 2001 it'll be a ko3S. especially if its facelift. ive not heard of any facelift TQ's with ko3 turbos, although it is possible knowing audi!