change = (event) => this.setState({[event.target.id]: event.target.value});

<Input type="text" name="name" id="name" value={this.state.name} onChange={this.change}/>

{
  name: "MyText"
}

{
  foo: {
    name: "MyText"
  }
}

<Input type="text" name="foo.name" id="foo.name" value={this.state.foo.name} onChange={this.change}/>

<Input type="text" name="foo[name]" id="foo[name]" value={this.state.foo.name} onChange={this.change}/>