anononetwo For sign-up, if not using a VPN or proxy to sign-up (I recommend either),Proton VPN states they use a cryptographic hash of your IP that they cannot reverse engineer. Again, goes to trust as with all VPNs.
In this specific case though, the statement they cannot reverse the hash is simply blatantly wrong. An IPv4 number is 32-bits of information. Less if you exclude IP ranges unlikely to be used for signups. Even if they store the number as h = H(ip), you could get ip from h by simply calculating the hash for every single possible IPv4 address, until you get a hit, which is feasible. In fact, you only need to do this once for all IPv4 addresses, and can then mass reverse all of them.
One may wonder why they store hashed IP addresses at all. Well, likely because they want to throttle number of signup attempts per IP address, for fraud prevention. This means they are not salting the values, and not using a slow hash function either, since they need checks to be quick. So, it probably is h = H(ip), and nothing fancier.
anononetwo If you use the paid Proton VPN (or Mail), they state they keep your name and last four digits of credit card for billing and VAT purposes and this this can be court ordered to identify you.
Just for completeness sake, Mullvad VPN also states they keep all billing details for 40 days or something, as legally required by consumer laws.
The whole point with VPN providers is that there should be no tie between your account and your activity. This is the no-log policy, they don't log anything that ties your account to your activity.
You account is used to authenticate you against the VPN server of your choice, so they can verify you have paid. The VPN server may log that you connected to it, both from which account and which IP address. Many people will be connected to the same VPN server at the same time. And information which VPN server is responsible for which activity on the internet, whether visiting a website, logging on to an account on another website through the VPN server, or file sharing and so on, is of course all over the internet in log files everywhere. But, if someone would come to your VPN provider and ask, "hey, we want to know which of all users who was connected to your VPN server A at 10:23 on 23rd of April this year it is that connected to website B". This, the VPN provider should not be able to answer. They can likely give the list of all VPN users that were connected to that VPN server at the time, but not say who of them it was that visited that specific website, since they didn't log that information.
Clarke Those who mention Mullvad, it's not free and not FOSS, making Orbot and Proton better options.
Yes, the Mullvad VPN client app for Android at least is fully open-source, and available through F-Droid, which do not accept proprietary apps.
benzo301 Do what you must with this information, but i assure you that if it's a company like Mullvad there is no "dilemma" with VPN.
Actually, Mullvad VPN was probably forced to give identifying information about at least one user at one point in time. Probably many. Mullvad VPN used to have a feature where you can configure in incoming open port, to aid peer-to-peer applications like file sharing. This created a link between the activity of users who did this, and their account, as all VPN servers needed to know which of all connected users to route incoming requests on a specific port too. Mullvad VPN quite abruptly removed this feature, stating privacy concerns, and that the feature is an "anti-privacy feature". At least rumors were that requests for information to Mullvad VPN started containing port numbers where known, ie "we want to know which user account are using this port number for external communication", and that information Mullvad VPN did have.