To be able to break into your router, someone would have to get past the the wireless security by either knowing the key or putting a cable in and bypassing it.
Neither is easy if you have the proper level of security so if you change anything, change that to a strong mixed upper and lower case alpha and numeric key and keep a note of it outside your computer. For my part, I would change the SSID state to Hidden or Not Broadcast and let the neighbours worry about their channel settings - most people don't anyway.
I once dealt with a case where we suspected someone had called at the front door and noted the security key off the back of the Sky router when the householder's back was turned. Change your key and that can't happen to you either.
Your neighbour obviously thinks he's smart, given his choice of SSID, but he's really only making himself a target.