If you see someone else on your router, you should do more than just change your SSID and Password, you should use the block MAC address, or better yet (but it’s a bit more to manage) filter by MAC address which only allows devices you own or authorize to connect to your wireless. You can easily find the MAC address for your computers and phones. I won’t go into it here, but just search for how to find out your MAC address, then put those addresses into your router. Also, the MAC addresses should be listed in your router as connected or previously connected devices. Filtering by MAC, while it is possible to get around, is more work than what it’s worth to steal someone’s home internet.
Changing your Router name access password does no good if you do not set up a password to the router setup. Anyone can get a default password to your router setup off the internet. Some routers require a hardwired connection to enter the setup. SOME DON’T. If you find you can’t get on the internet anymore, you might check your router to see if some one has hijacked it.