Part of my convertible top is busted and I need to know what it's called.,.any ideas?

I can't help on the id of the part but you could go by your local VW dealer and I'm sure they can get you the parts you need (be sure to have your VIN #). You can also; look up parts online:

check out:

VW Parts | Volkswagen Parts

Volkswagen Parts 2Go | Genuine VW Parts | Up to 25% Off

or vw's online e store:

Volkswagen National eStore

It looks by the picture that you are looking for the guide that slides the headliner back and forth as you lower and raise the top. It has a couple of cords that attach to the clip and go through guides. Depending on the part or parts that are broken sometimes its easier to just replace the broken pieces, but you will have to purchase the complete guide, cost is about $40.00 at your dealer, best to go with your VIN as suggested above as there are two slightly different versions of this clip but I think you have the early version.

If correct you are looking for part number,
Left side 1Y0 871 341
Right Side 1Y0 871 342
Later versions are the same part number but add a "B" to the end.

Look at this link from ECS.
Search 1Y0871341 - 1Y0871341 - GUIDE - ES#325451


Hope this helps...

K