So, to be clear here, BTC wallets don’t have a name tied to you. The financial system has just put exchanges on lockdown with existing KYC rules so you can’t buy BTC or other crypto currencies without going through a KYC process. Then the first deposit into a wallet is tracked because it’s the same amount, which corroborates the purchase of crypto. Then everyone knows that wallet is yours and can track from there where that money goes.
Also, if you’re talking about taxes, which this doesn’t seem to be a tax question, you are only taxed when you exchange BTC back into a national currency. That’s a problem for Future You.
Some Bitcoin ATMs require scanning a government ID, palm scan, etc. so even if you’re using cash at one, you’re still likely to go through a KYC process which will declare the purchase to your government. Really, what you’re trying to do is circumvent KYC processes, which vary by country but are often very strict. Doing something stupid like using a fake ID at a Bitcoin ATM will be a very quick way to find out how much your country cares about this kind of thing and how quickly they can track you down.
If it were me, I would first use ChatGPT via Duck.ai to explore my local KYC regulations to know what the options might be (check sources!). We can’t tell you without knowing what country you’re in, and I don’t want to ask you to give that info up. If your daily purchase limits without triggering government overreach are reasonable, consider just working slowly and going that way with normal exchanges. Also look to see if your country’s policies are poorly worded and ONLY track BTC and not other coins. It’s unlikely, but it might be a workaround.
If you live close to another country or plan to visit another country with Bitcoin ATMs in the near future, using one outside of the country where you’re taxed might be a slightly better option. My best guess would be that your name would still end up in some database of people owning that wallet and if the two countries talk, then you might end up penalized for not reporting if that’s a thing where you live. Maybe, maybe not. That is likely a crime in some places, so do not do anything illegal. It also might only be a requirement to report it if you pull BTC out if there’s capital gains, so you need to do research on this.
Next, I would seek out someone local to you that knows about BTC and has a wallet and ask them what their thoughts are. They may be able to help you out, and may suggest something like paying a real human cash for BTC, which is very risky if it’s not fully illegal where you are. If you end up in that situation, start off small, with 10% of what you want to buy as a test, and just expect to lose that money. If you end up getting the cash into your BTC wallet, then break up the remaining 90% of your cash into 3 more purchases, but tell them that you’re making 5 more purchases, then after the 3rd one say you decided that was enough and needed the rest for something else. That way if they want to keep your last tranche to screw you, you’ve stopped before they can do that.
A lot of these are bad options, might cost you a lot in transaction costs that are humans putting the squeeze on you, and some might be illegal where you are. Be aware of local laws and be careful.