JSFiddle - React, Tailwind, and code Playground

HTML

<select id="mySelect" onChange="check(this);">
    <option>Choose Your Name</option>
    <option>Frank</option>
    <option>George</option>
    <option>Other</option>
</select>
<div id="other-div" style="display:none;">
    <label>Enter your Name
    <input id="other-input"></input>
    </label>
</div>

JavaScript

function check(elem) {
    // use one of possible conditions
    // if (elem.value == 'Other')
    if (elem.selectedIndex == 3) {
        document.getElementById("other-div").style.display = 'block';
    } else {
        document.getElementById("other-div").style.display = 'none';
    }
}