JSFiddle - React, Tailwind, and code Playground

HTML

<select id="choose">
    <option>Choose Your Name</option>
    <option>Frank</option>
    <option>George</option>
    <option value="other">Other</option>
</select>
<label id="otherName">Enter your Name
    <input type="text" name="othername" />
</label>

CSS

#otherName { display: none; }

JavaScript

$(document).ready(function() {
    $("#choose").on("change", function() {
        if ($(this).val() === "other") {
            $("#otherName").show();
        }
        else {
            $("#otherName").hide();
        }
    });
});