W7 64 bit Network issue

[#1]

So far all else seems ok.
Internet access is fine except that in the Network and Sharing Centre I can see:
myown-PC=== Network===Internet
although on the laptop it is
Laptop-PC===mynetworkname===Internet (laptop is also W7 64bit
A copy of the network map is added below.
I can transfer files across the network without problems but it is strange that the PC is showing as unknown network.
I have checked the settings in  System Properties and the Workgroup name is the same for both PCs. When I just set up the PC it reqiuested the Network passowrd which I obtained from the laptop.
I've tried setting up a new network again but where is says 'Choose the wireless router or access point you want to configure' underneath the message 'It might take up to 90 seconds for unconfigured sevices on your network to appear.' there is nothing showing.
I've looked at every conceivable setting I can think of but can't see why the PC is not showing under the same workgroup as the Laptop.
Any advice would be appreciated.

[#2]

I have this too, a difference between my laptop and desktop machines.
I think this is the reason:
When the desktop PC connects, it shows "network", and so did the laptop the first time I used it. I connected via network cables to my router.
But I set up the laptop to connect to the same network via wireless, and the laptop now shows the name of my wireless network instead of "network", even though I'm connected with network cables and not via wireless.  I suspect Windows has remembered or assumed the network name as the subnet addess and routed mac address would be the same in both cases.
So, in your case, I guess that mynetworkname is the wireless network's SSID, and "myownpc" has never connected on that wireless network?

[#3]

Quote from: KenA

So, in your case, I guess that mynetworkname is the wireless network's SSID, and "myownpc" has never connected on that wireless network?

You're absolutely right.
The desktop PC has never connected wirelessly as I prefer to have at least one computer wired.
In other words, there isn't a problem just the way Windows 'labels' the network on each PC?

[#4]

Yes, that's my theory.
My laptop shows the name of my home wireless SSID.  I'll be in the office next week, and will try to connect my laptop to the office wireless network, then just via the wired network, and will see if it updates.  I'll let you know.