The name change, which comes into effect on 2 July, highlights how the charity works with people suffering from all forms of mental illness. Its full name will be Rethink - severe mental illness.
The change has been approved by a clear majority of the charity's 7,000 members, 7,500 service users and 1,500 staff after a four-year consultation period.
Paul Farmer, director of public affairs at the charity, said: "I don't believe that there is an organisation in the public, private or voluntary sector that has consulted so widely or deeply about the work it does and the image it displays."
The name change will be accompanied by a campaign to expose mental health waiting times.