Earlier quoted context omitted.
As far as I understand, BlaBlaCar has some centralized controls on your identity since payments go through them and changing your payment info is not quite as easy as making up a new nickname. That's a big difference to an anonymous-by-default cash-only network.
They operated for years without accepting payments, the payment is a recent thing.
However, when I was using the service it was quite common to get the drivers number and contact them directly for the "next" time.