The username that you changed was the login name to get into the router software.
The name that you see when you click on the icon in the bottom right is the SSID ( Service Set Identifier )
This is the name of your Wireless Network - it is broadcast by your router.
The names of other networks that you can see ( your neighbours ) are their SSID being broadcast by their routers.
It is possible to change the SSID - but this will not make the router any more secure.
No.
If, when you connect to the network for the first time, you are asked for a Network Key ( password if you like ) then your network is secure.
The time to worry is if the network shows as "Unsecured" - then we need to do something about it.
No - not at all.
The username and password that you have changed is the one that gives you access to the router settings - nothing else.
I hope this clears things up for you ?