Updating state with props on React child component

It would also be good to check if you even need to update the state, since this will cause a re-render.

componentWillReceiveProps(newProps) {
  if (this.state.name !== newProps.name) {
    this.setState({name: newProps.name});
  }
}

Calling setState() in componentWillReceiveProps doesn't cause additional re-render. Receiving props is one render and this.setState would be another render if that were executed within a method like componentDidUpdate. I would recommend doing the this.state.name !== nextProps.name in shouldComponentUpdate so it's always checked for any update.

componentWillReceiveProps(nextProps) {
    this.setState({name: nextProps.name});
}

shouldComponentUpdate(nextProps) {
    return this.state.name !== nextProps.name;
}

You need to implement componentWillReceiveProps in your child:

componentWillReceiveProps(newProps) {
    this.setState({name: newProps.name});
}

Edit: componentWillReceiveProps is now deprecated and will be removed, but there are alternative suggestions in the docs link above.