They can easily find you via IP. If you use Discord, you give them your IP. This IP is handed out to any law enforcement organization and from there it's trivial to find your ISP and from there, find out who and where you are. I'd be surprised if the entire process isn't automated tbh. You'd think that these various corporations would not give your data out willy-nilly but in reality they don't give a shit and are woried they'll get sanctioned by governments if they don't cooperate blindly. Which yes, governments did in the past to companies with concience.
Next time police come without a warrent you can shut the door in their face and tell them to fuck off unless they have a Warrent singed by a judge. You have that right as a US citizen.
Actually the case in many EU countries too. Police is specifically trained and exprienced in making you think they have rights they haven't. When I read here that police comes to people's homes and e.g. search them for things like SN with no court order... well I can't say I'm shocked because that's how the government thugs operate, but you don't have to cooperate.
Don't talk to the police. Don't answer questions. Only give them your ID when asked. Repeat that you would like them to leave. Stay friendly, but persistent. If they come in anyways, don't sign anything. Don't agree. State clearly (and best, with a witness) that you have not agreed to a search.
I understand it's easier said than done, especially since they're also trained in intimidating you. But it's the proper way to do it.