The claim under examination: consciousness is nothing more than the brain, so when the brain dies, the person is gone for good.
Standard · preponderance of the evidence, not proof
The verdict
Brain dependence during ordinary life is strongly supported. The further claim that death certainly ends all consciousness is plausible, but not established by the evidence here.
If you read nothing else
Materialism explains one thing very well: our conscious life is deeply tied to the brain. Any theory of a soul has to account for that. But dependence is not the same as identity, and near-death research has not shown a mind working apart from the brain. Death may be the end. It has not been shown to be.