Thomas the Apostle claimed he wouldn't believe in the resurrection until he actually touched the wounds of Jesus.
Jesus understood Thomas' doubt and invited him to do just that. But according to the Gospel of John, Jesus also included this gentle rebuke: blessed are they that have not seen, and yet have believed. (John 20:29)
Either way, Thomas lost his doubt. But doubting Thomas came to name any incredulous or habitually doubtful person.
For example, consider the person on Twitter who confessed, "I am slowly turning into a doubting Thomas about social media."