We had a router with a open wifi signal that had gotten slow, and got a new router which gave us a new wifi signal and we successfuly secured it. Though the old open signal still shows, and is accessable in the wifi connection window. Is it possible to remove the old signal so that it can not be accessed by future users? And if it is not removable, would having multiple signals like this slow down the secured wifi that we are currently using?
First, are you certain that the open broadcast network name (SSID) is actually coming from your router and not from a neighbor's router or a public WiFi hotspot ? As a test to determine if it is actually broadcasting from your device, unplug it and see if that broadcast name disappears. Then plug it back in and see if it reappears. If it does, then you'll know that it's yours.
If you've removed the old router, any network associated with it should be gone. You're not talking about the "xfinitywifi" network, are you?