My own strategy is to assume it is a scam regardless of which ISP, or CP, they claim to represent. They are after all just guessing, and might sometimes guess correctly.
Even if they correctly guessed my ISP was Zen, and they claimed to be calling from Zen it'd still be safe to assume it was a scam, and nothing they could say would ever make me doubt it was a scam. I simply don't believe any genuine ISP or CP would contact a customer in that way.
That said, I know that BT do actually cold-call landline customers to remind them of overdue bills. I have received such a call myself and even though I knew it might be genuine, I simply explained to the caller that "You are probably a scammer and so I am disregarding everything you say to me". They tried hard to convince me and got quite annoyed with me for refusing to trust them but I stuck to my lines, they eventually gave up, and nothing bad happened other than a letter through the post reminding us to pay.