Short answer: The Nintendo 3DS doesn't have an SSID. An SSID (Service Set Identifier) is simply the name of a wireless network—like "HomeWiFi" or "CoffeeShop_Guest." Your 3DS connects to an SSID; it doesn't create one.
When you set up internet on your 3DS, you're telling the console which existing Wi-Fi network to join. You'll scan for available networks, select yours by its SSID, then enter the password (if secured). The 3DS stores this profile so it can reconnect automatically.
Think of the 3DS like a laptop or phone: it joins networks; it doesn't broadcast them. If you're trying to connect, you need the SSID and password of the Wi-Fi you want to use.