...Or someone in the "household" has another computer using the same Computer Name? Are you looking at the list of devices that have been connected to it in the past or currently connected?
If in the past you have connected your computer to the router once wired and once via wifi. You will see two different MAC addresses on the list of devices that have been connected to it. If you are currently connected to the router only on wifi or calbe (not both) and both are showing to be actively connected and no one else in the household is connected to it using the same "Computer Name" follow the steps below.
If in case you think someone unauthorized is using your Internet/router or you just want to secure it a bit more;
1. Change the password to your router. (Long random password)
2. Change the password to your wireless network and use WPA2 (Long random password)
3. (If your router supports it) White list the MAC addresses of the devices that are allowed to access your router. This will block any "new devices" trying to gain access to your router.
Hope it helps, good luck!