You will need to provide a lot more information prior to getting a truly useful reply. Otherwise, only general advice can be given. Also, you will need to work on this systematically, there is no single "press here, use that tool" recipe.
First, you must be sure where the problem is. You think the neighbour "steals your Wifi", alright, so let's formulate the problem as "something Wifi", and get back to "stealing" later.
First of all test with Wifi turned off and an ethernet cable attached to the router.
Problem gone? So the problem is really within the "something Wifi" realm.
Problem persists? Not related to Wifi, stop searching there!
Next, you need to be sure that what you see is not "perfectly normal" because you are in some way using a shared-bandwidth channel (such as every back-channel cable modem because that's just a technical limitation, the majority of 4G/5G, and a good number of cheapish DSL providers).
For example, being with a cheapish DSL provider in a third world country such as Germany can imply that it is perfectly normal if your 100MBit/s link suddenly drops to 70MBit/s for no apparent reason. That's because they acquired a few extra customers in your neighbourhood, and they didn't book enough bandwidth on the fiber backbone, so they're just reducing bandwidth silently. As long as nobody complains, they leave it there. Sometimes, reconnecting and getting a different slot in the DSLAM "magically" fixes it. Whatever. Such issues are annoying, but they can be very real, and they're unrelated to your neighbour. Same for cable modems. Neighbour starts to download porn, and your bandwidth drops. That's normal. It's just how the technology works.
Now, assuming the problem is indeed gone after using an ethernet cable, what's next. First, of course, your neighbour may indeed be stealing your internet bandwidth, but you should be sure that's acutally the case before burning down his house.
There are many ways Wifi can be slowed down (regularly, accidentially, and deliberately). First, your neighbour may have his own WiFi, and all networks on the same channel influence each other. Additionally, neighbouring channels can be, and usually are affected, too (often several of them!). Depending on channel width and clever or not-so-clever channel selection, this can range anywhere from "who cares" to "total desaster", in normal operation. And, this is entirely legitimate.
Also, devices and the type of protocol that they use on the same channel, play a role. A "typical" 2.4GHz router supports 802.11 b/g/n by default, unless told otherwise. Which is actually a really stupid choice because if you have a single "b" device nearby, you're down to 11MBit/s for all devices. Then there's microwave emitters such as actual microwave ovens, or seemingly harmless microwave emitters such as e.g. cheap LED lightbulbs, or a Playstation. Neighbour comes home, turns on light, Wifi dies. That's actually possible! Depending on what exactly it is, that is not "legitimate" in most countries, but you will have to find out first.
Now, you said that you even tried to turn on WPA, which is funny because not only is WPA very outdated (even WPA2 is on its way being phased out) but it sounds like before that you didn't have any such thing as a Wifi password at all?
Now you should know that while WPA2 is subject to e.g. KRACK, which is, in layman words, a way of eavesdropping communications, it is reasonably safe against being "stolen" otherwise. The eavesdropping is not normally a problem because the internet itself is unsafe, so anywhere it matters, you use TLS anyway. Only just, accessing your router's admin panel via Wifi (telnett, likewise), and consequently entering your password for everybody nearby to read, is not such an awesome idea for that very reason. Cable, please. Ethernet cable. Only. Ever.
Apart from that, WPA2 is reasonably safe, except, well except most routers have WPS enabled by default.
What's that? It is a functionality that makes setup more comfortable (press button method). Unluckily, it is also something that is trivial to brute-force (4-digit PIN), and for which there exist tools that let anyone break into your WPS-enabled network within a minute. Every no-shit router has an option to turn WPS on only temporarily on demand, and restrict access to already known devices otherwise. Do that. Even if your neighbour isn't stealing your Wifi, still do it. Just, because.
So you change your password and an hour later you feel like someone is stealing your Wifi again? That looks just like them exploiting WPS. Turn WPS off, change password, and see what happens. Problem gone? There's your answer.
Rule out possible causes one by one that way. If disabling WPS didn't change a thing, look how many wireless network SSIDs you see advertized in your network connections pane (or in the tray). No tools needed.
If there's like two dozen of them, it's clear why internet sucks at times. If there's just you and nobody else, it's a bit suspicious. Etc. etc.