|Typically you don't "see" the device, just the SSID (WLAN).|
If your range extender is using the exact same SSID and encryption key as whatever device you have making your WLAN now, then you should just connect automatically with your phone when the extender's signal is significantly stronger than the other WLAN device's.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.