I realise that this question is subject to local trends (and I'm in the US), but I encourage people in other countries to submit their methods!
How do you accept packages/deliveries anonymously? Of course, there are mail redirection services, but a third party which corroborates with different parts of the chain can likely figure out your identity and what you have purchased/have incoming.
I haven't been able to find a good solution to this yet, and I believe the new rule in the US is that the receivers identity must be reported to the government? This (or a variation of this, I don't remember) is a recent event.
I know I might not be relevant because I am not in the US (and in a big city), but I pretty much always order from online stores to the stores' offices. Not only to not surrender my address, but also because usually they allow paying in cash upon reception (big Amazon-like aggregators are an exception but I usually avoid them), and this also does not cost extra unlike a delivery to your door.
In Europe, many merchants allow you to order online and collect (and pay for) the goods from their premises. For example: https://www.galaxus.com/en/wiki/556