I am starting a new website and would like to protect my privacy. I am thinking about using a Paypal account to purchase my domain and hosting, as well as for monetization further on. How easy is it for someone to figure out who I am through my Paypal account? I would like to protect my identity as well as possible with this new website.
Disclaimer: I am not a lawyer, this is not legal advice. Please consult a lawyer for any specifics on the follow
The steps to anonymity yourself vary depending upon from whom you want to hide. PayPal or any financial institution wants to know who they are working with (and in some cases legally mandated - KYC). If you just don't want random people to come flame you, "swat" you, etc. Then PayPal is not really your concern because its not like someone is going to call them up and they are going to tell them who you are. However, a government could likely request records from any business to find out who their customers are.
Beyond that, you would also need to protect your identity from the web hosting and domain registrar companies. And also use anonymity strategies (e.g., TOR) when uploading or posting to your website. You will need to publish
whois information for your website, but you can use privacy services that will hide that from the public.
Running a business you will likely need to give out a mailing / billing address at some point. You can get a PO Box or mail drop service, but there would still be records about your registration of such with the mail services in many cases.
It also sounds like you plan to setup this website as an "individual", but you may want to take advantage of a corporate structure that offers a high amount of anonymity that at the very least would be very difficult to unravel to find out who you are. You could for example setup a Delaware or Nevada corporation and have that own another corporation etc to create layering. You should be able to setup such structure legally, but it can get expensive and complex. You then conduct all business for the website through the corporation. Clearly, you should find an attorney you can trust.
If your concern is really just PayPal, perhaps you can buy a prepaid card with cash and use that for the purchase transaction. You will still need to give contact data at some point likely though.
Being a business man / woman requires that you give up some privacy. Namely the people you do business with need to know who you are for legal and other reasons.
Ergo what you want is not facilitated currently in any way shape or form on major platforms like Paypal.
You could try and find a Hosting partner that takes Bitcoins but IANA does require a Name and Address for DNS registrations (it does not require these details published through a WHOIS however)
Also talk to a lawyer in your jurisdiction, as there are often laws in place requiring you disclose your name and other details to potential clients.
While googling this, I stumbled upon this. There are options about what information is given to payers. I haven't read through all of it, but there are detailed steps on how to obfuscate your private information when receiving payments.
My personal guess on this is that if one really wants to know, he/she might be lucky contacting PayPal's support and doing some social engineering - e.g. report your account as "abusive" only to be then notified by the support that the account belonging to "your name" is in fact not abusive - having leaked your name.
If you depend on truly anonymous paying methods, try cryptocurrencies. e.g. Bitcoin or Ethereum. A crypto-wallets address doesn't necessarily require any information tagged to it - PayPal requires a lot of Information, which of course, may leak.