offline file question

I have a laptop with Vista Business and a dektop running XP SP3. Since I
travel frequently, I had set up a foder on my desktop, let's call it "synch",
and I store all my files that I might need on he road in that folder (and
subfolders). I then had connected to that folder from my laptop and "made the
files available offline". This worked really nicely.
Then we moved, and IT found it necessary to rename both my laptop and my
desktop. Of course, nothing works anymore. I can connect from my laptop to
the desktop, and I can now select that folder and make it available offline
again, but will that then be an offline folder in addition to the old one?
How can I delete the old offline folder and recoup the storage space? I know
the old filesa are still there, because I used an image in the synchronized
folder as my desktop background, and when I pretend that I want to change it,
it still goes to the old address. But the old computer name does not show up
anymore in the network.