Computers identify different network?

All my computers are on the same network (some wired and some wireless) but they show that they're attached to a different network. This is indicated by the name of the "little house" in the network diagram.

What is going on?

No - there are two other names indicated on the small house on each separate computer.

The "I-HATE-NJ-AND-NYC" is the only one I have.

This is a picture of the whole network layout (I only have one switch...confused on that point):

Checked, there is only one. I'm thinking each device(switch, router) may have its own identity? The Homegroup instructions state that a Homegroup will not work if a network has more then one name/network. But, I don't know what would account for the third name, I only have one router and one switch.

I just saw this and it is very confusing. The Vaio Laptop's network layout is in the picture below. I have Fios and I think the Verizon router has an internal switch, so in addition to my external switch I'm seeing the routers internal switch? But, I still have no idea why I have three network names.

Anyone know what is going on?

This is still driving me NUTS. Is these any way to delet all the home-group settings and find the other network?

Any Ideas?

See this tutorial by Brink:
Network Name and Icon - Change
You can try the Merge or delete network locations on the page where you can change the name.
I'm not sure what it does, i never used it.

I also found this:

There is variety of "Names" involving the Network aspects of the OS.
It comes from the Group name, Computer name, Wireless SSID, Router's Network Name, Network name, the Local Area Connection name, and the ID of the Local Network Connection.
All but the latter can be easily Renamed.
By default Windows assigns to the connection name “Local Area Connection 1”, and every time a change is made, it advances the number.

Source: Wireless Network "name" mislabeled as "name 2" - Microsoft Community