Changing Network Name

Have you installed the Airport Utility software? To change the name of the network just go to Airport>Wireless>Wireless Network Name. For the other questions, I'm not sure.

1) The base station does not have an on/off switch. It's OK to leave it on all the time?

Yes, it was designed to operate 24 x 7.

2) My set up yielded two networks, my network and one guest network. Do I really need a guest network, if it is just me and my wife using the network? How do I eliminate the guest network?

No, the guest network would be totally optional. You decision to use it should be dependent on your networking requirements. You can safely disable it without any affect. To disable it, you would need to use the AirPort Utility. (ref: AirPort Utility > Select the AirPort Extreme > Manual Setup > AirPort > Guest Network > Enable guest network (not checked))

3)I created these two networks using my real name, not realizing that they would show up as such when people scan for wi-fi access in my vicinity. How do I change my network name without messing up my set up?

Again, you would use the AirPort Utility to do this. (ref: AirPort Utility > Select the AirPort Extreme > Manual Setup > AirPort > Wireless > Wireless Network Name)