How to add a value to an array inside a React state

I have a React Component where I have a Form with multiple Selects. The options of these Select components is passed to the SearchComponent as props.

I want to store the selected options in local state, and once the Submit of the form is pressed it is sent to the parent component that passes a function as a prop - searchStatements.

Since the select is multiple, I have an array of all the options that can be selected and stored in state.

class SearchComponent extends Component {
    state = {
        companies: [],
        years: [],
        currencies: []
    };

    render() {
        return (
            <Form
              onSubmit={(e) => {
                  this.props.searchStatements(this.state.years, 
                          this.state.currencies,this.state.companies);
              }}
            >
                <Select
                  multiple=true
                  value={this.state.companies}
                  options={this.props.companies}
                  onChange={(e) => this.handleSelectChange('companies', e)}
                />
                <Select
                  multiple=true
                  value={this.state.years}
                  options={this.props.years}
                  onChange={(e) => this.handleSelectChange('years', e)}
                />
                <Select
                  multiple=true
                  value={this.state.currencies}
                  options={this.props.currencies}
                  onChange={(e) => this.handleSelectChange('currencies', e)}
                />
            </Form>
        );
    }

    handleSelectChange = (name, v) => {
        if (name === 'currencies') {
            const newArray = this.state.currencies;
            newArray.push(v);
            this.setState({'currencies': newArray});
        } else if (name === 'companies') {
            const newArray = this.state.companies;
            newArray.push(v);
            this.setState({'currencies': newArray});
        } else if (name === 'years') {
            const newArray = this.state.years;
            newArray.push(v);
            this.setState({'years': newArray});
        }
    };
}

The initial state is like this -

state = {
    companies: [],
    years: [],
    currencies: []
};

When a currency USD is added, it should become

state = {
    companies: [],
    years: [],
    currencies: ['USD']
};

Again, when a currency GBP is added, it should become

state = {
    companies: [],
    years: [],
    currencies: ['USD', 'GBP']
};

However, in the handleSelectChange(), after adding a couple of options, it becomes something like this -

state = {
    companies: [['GOOGLE'], ['GOOGLE', 'FACEBOOK']],
    years: [],
    currencies: [['USD'], ['USD', 'GBP']]
};

How do I change handleSelectChange() such that my final output looks something like this -

state = {
    companies: ['GOOGLE', 'FACEBOOK'],
    years: [],
    currencies: ['USD', 'GBP']
};