If you use Mullvad you get a token instead of an account. It’s not linked to any email address. You can then pay directly to this token using crypto. You can even send cash in an envelope. If you use Tor to get a token and pay, you’re as private as can be.

The thing however is that VPN providers can always see what IP address is using their service. So however private your account and payment is, in the end you always have to trust the provider that they are not logging IPs.

If you are buying from Mozilla, then both Mozilla and Mullvad get access information. This means that buying from a reseller is less private by default.