Updating an object with setState in React

Is it at all possible to update object’s properties with setState?

Something like:

this.state = {
   jasper: { name: 'jasper', age: 28 },
}

I have tried:

this.setState({jasper.name: 'someOtherName'});

and this:

this.setState({jasper: {name: 'someothername'}})

The first results in a syntax error and the second just does nothing. Any ideas?