There are two different passwords that access different functions. If an attacker has the admin password, then he / she can change the SSID, WiFi password, and any other settings on the WiFi router.
To fix: ensure your WiFi security setting is WPA or WPA2. Then change the WiFi password to a long one (at least 12 characters, more is better) with special characters and numbers (such as #, $ %, !, 1, 6, see for example Is there any point in using 'strong' passwords?). Also, make sure the admin password on the WiFi router is changed from the factory default. This admin password is different than the WiFi password. It should also be a long complicated password, but do NOT make it the same as the WiFi password. The WiFi password is the one you give to friends and family to access your WiFi. The admin password should be kept with you only, or people you REALLY trust, as it can be used to change WiFi settings. Once this is done, change the SSID back to one you like.
Also, make sure to disable the feature called Wi-Fi Protected Setup (WPS). See http://www.howtogeek.com/176124/wi-fi-protected-setup-wps-is-insecure-heres-why-you-should-disable-it/ for details on why WPS is not recommended.
If the attacker is still able to change the SSID and any passwords, your system is more deeply compromised and I would recommend contacting a computer expert or store who can help you clean your system. They can also give you advice on if there is anything local law enforcement can do, as your attacker is likely committing a crime.