Is it "the payment has come through" or "the payment has gone through"?
Either is acceptable. The context would perhaps vary: if I was expecting a payment, and it arrived, I might say 'The payment has come through'. If I was sending or making a payment, and I saw it had left my account, I might say it has 'gone through'. But a recipient might also use 'gone through'.
To say "come through" is to imply that you are the recipient or that the recipient is involved or referred to. "Gone through" could be used by anybody.
To clarify, as the recipient you might say "The payment has come through" or "I will ask the recipient if the payment has come through", while if talking to the recipient you could ask "Has the payment come through?". If you were not the recipient and were not either talking directly to the recipient or referring to them, I feel that "gone through" would be more appropriate.