Somebody hacked my router and changed my wifi SSID
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.
Ok I am changing my answer after reading all the comments. You need to understand the basics:
SSID = The SSID is the name of the wireless broadcast from your router. This is not a username.
If the person keeps getting in then its possible your security is not WPA2 like you think it is. or your password for the wifi is really weak or common. try a randomised password.
If he can connect to your wifi, he can connect to your router through a web browser. Typically the address to access a router in the browser is 192.168.0.1 OR 192.168.0.254 OR 192.168.1.1 OR 192.168.1.254 .... (to get the address more officially rather than guessing, open up command prompt in windows and type: ipconfig /all and look for your default gateway related to your network settings)
Upon accessing the router through the web a DIFFERENT password is used, if you use a netgear router the password could actually not exist and the user name will be admin.
When into the router you can change things such as the SSID easily.
How would I solve these issues?
Reset the router to factory default.
Change the router user name and password (NOT THE SSID)
Now change the SSID and make the wireless password / encryption a randomly generated WPA2-PSK.
A firmware update
If this fails, follow these steps, reset your devices as he may have bugged you in someway.
Change your security to block ALL devices, except MAC addresses of your own gear. You'll have to look them up and enter each one manually. But the change should stop him cold.