Вы можете вызывать функцию с onValueChange
измененным каждый раз, когда
<Picker
selectedValue={this.state.firsname}
style={{height: 50, width: 100}}
onValueChange={(itemValue, itemIndex) =>
this.yourfunc(itemValue, itemIndex)
}>
<Picker.Item label="John" value="John" />
<Picker.Item label="abc" value="abc" />
</Picker>
<Picker
selectedValue={this.state.lastname}
style={{height: 50, width: 100}}>
<Picker.Item label="Deep" value="Deep" />
</Picker>
//set your selectedValue to the state where you save the value
....
yourfunc = (val, index) => {
//doing some stuff to change another picker
let lastname = //get lastname from val
//and then this.setState lastname
}
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