Home Networking

[#1]

Wireless.  Login to the router and change the SSID to something you like.  Wired only has the name your OS assigns.

[#2]

as the previous poster indicated normally you assign network workgroup name within the Operating System

There is a network name that can be set within the VZ Router:

Logon to Router Choose Advanced Tab at top

Choose System Settings

Local Domain - set name

[#3]

You need to be more specific.  What OS?  Wired or wireless?  Where are you seing the name that you want to change?

On the off chance that you are using W7 with wired connection, just open the Network and Sharing Center and clik on the house.