Networking XP Pro Laptop with XP Home PC

I have been beating my head on this all day. My home desktop has Windows XP Home, as I had no need for Pro at home. Now, I want to share files between my home desktop and my laptop — which has XP Professional.

I can access the laptop from the desktop and view/get files.

I can ping the desktop from the laptop by IP.
I CANNOT ping the desktop from the laptop by name.

Also, when I search for computers on the network by IP, my laptop does not see the home desktop.

Basically, I seem to be having a problem with name resolution from the laptop (PRO) to the desktop(HOME).

Any thoughts?

Best!
Scott