I looked at that part on my '08 XC70.

it certainly looks like a separate part, held on by two clips at the rear door edge.

I'll bet that you remove it by opening the door and window and push the part toward the rear of the door.

It looks like you install it by sliding it back on - there may be tabs and slots in front to hold the front tight - check for slots at the top and bottom. The clips at the rear are to add friction to hold the part in place.

If the clips are damaged, you may need new ones.

Procedure 1. Install the piece with the window open. Put some dish soap on the entire seal, and on the window to help the window slip up the first time.

Procedure 2. Install with window closed. MAKE SURE THS RUBBER SEAL IN THE FRONT IS FLAT BEFORE YOU PUSH IT ALL THE WAY ON. Put some dish soap on the entire seal, and on the window to help the seal slip over the glass

As for its name - the B pillar would be the part of the body that remains after both doors are open. How about - Front door, rear of window trim?

See my other post.