My MAC address has been spoofed by a neighbor to access my WiFi, positively. I know it's futile changing the WPA key or not broadcasting the SSID.
What are my options at this point ?
You mention that in comments that you are a novice and it appears you do not understand wireless in any great deal. You also don't provide a lot of information so your "problem" is very vague.
When a device associates to a wireless network, it goes through a number of steps. Among these steps there is an "open authentication" which normally is simply a two packet exchange. This is where MAC authentication takes place if configured. If the MAC is configured then the open authentication will succeed, if not it will fail.
Once the open authentication is done, the WPA2 handshake takes place. This is where your device and the wireless access point negotiation encryption making use of the PSK. Even if a device is allowed in the MAC filtering, it still must complete this handshake before it completes the association to the wireless network. If the handshake fails, the client is disconnected.
Once associated, the other semi-common place that MAC filtering can take place is if you have some sort of captive portal. These are not common in most home networks and may have seen these at businesses that provide public wireless access. Once you connect to the wireless network (which generally is an open network or doesn't use any sort of PSK), you have to login/click through a web page before you can connect to the Internet (or anywhere else). It is only in these cases where MAC spoofing will allow any sort of "unauthenticated" access.
So, if you are using WPA2 with a PSK, then simply MAC spoofing will not be sufficient to let your neighbor connect to your network. If you have a sufficiently strong PSK and have WPS disabled on your router, then you should be fine.
Steps I would take if I was hired to simply remediate this problem:
Note: Without knowing exactly which hardware you have this is a general list and some steps may not be applicable or even possible with your device. There may also be additional steps that are required depending on the device.
I had applied MAC filtering and the neighbor revealed to a non-tech friend of mine that he spoofed my MAC address. Do you think he's lying ?
Possible. I have known a few people in recent years who get some sort of amusement out of their own limited tech knowledge and something like a joke/prank app to fool their non-technical friends or acquaintances that they could accomplish a number of wireless (or other types) of "hack." These types of apps make it "appear" that they can do all sorts of things without actually doing so and it can leave their non-technical friends amazed at what they can do and make them fearful of what others are doing to them.
Or your non-technical friend could have completely misunderstood and/or miscommunicated their conversation with your neighbor. If they didn't really understand/follow the conversation, they could easily mix up different aspects of it and walk away with a misinterpretation of what was actually said.
Or our neighbor really did reveal that they are doing this. But your network would have to be using one of the two types of MAC filtering mentioned earlier as the primary means of "security" for accessing your network. If you have WPA2 with a PSK enabled, then your neighbor would also need to do more than MAC spoofing to get access to your network.
If your neighbor is using your WiFi, the fundamental problem is that they have your password.
Change your router password to a strong password and make sure you use WPA2 authentication. Make sure you perform the router change from a wired connection and disable WAN side administrative access.
Spoofing your MAC address would be a poor choice for them because it would result in collision problems with your MAC, which would not work well for either of you.
MAC spoofing would only come into play if you have applied MAC access controls to your router, which is not a default setup.
Last but not least, duplicate MAC addresses can be difficult to detect, so I would suspect spoofing your MAC is unlikely. Again, it’s probably just your password.