That is increasingly hard to do these days. Verified addresses etc are now minimum requirements to get the handset.

Of course you can pay cash and make up an address

Where I live they make a copy of your ID when you buy a SIM. So you'll also need a fake ID. And then there will be a copy of your fake ID with a photo of you on file somewhere, which could lead to some issues if the authorities discover you used a fake ID.

Where I live (USA), it's as simple as walking into a Walmart, pulling a plastic encased kit off the shelf and paying for cash.

No muss, no fuss. Just activate it at the on-prem McDonalds and you're golden*.