I am not sure if this is possible but is there any way to change the name of your wireless router to for when it shows up on the top of your phone to something besides what it is named?
Go to your connections. Click on "wifi network" & then click on "saved wifi networks" at the bottom. Highlight the wifi network you want to change the name of & then click the menu button. Click on edit in the menu options & then change the name. Simple, yet hard to find. I had trouble finding it when I first got this device earlier this week.
The name you are attempting to change is the network name, which is what the display is showing and is accomplished on a computer connected to the network. Router name is not going to change that display.
I had a completely different understanding of what the OP wanted to accomplish. It seems to me she want to personalize how various networks appear on the wifi display on her phone which is covered in the instruction manual that came with the phone on page 246 as I've previously referenced. Sure, you can change the SSID on your own personal network but you won't have that option on other networks.