JSFiddle - React, Tailwind, and code Playground

HTML

<ul class="dropdown-menu">
    <li>
        <a href="hoge">
            <span class="hoge" aria-hidden="true"></span> 
              hoge1<!--とりあえず、ここの文言のみを変更したい。-->
        </a>
    </li>
    <li>
        <a href="hoge">
            <span class="hoge" aria-hidden="true"></span> 
              hoge2
        </a>
    </li>
</ul>
<input type="button" value="追加" onclick="add('hoge3');" />

JavaScript

function add(text) {
    var whole_hoge = document.getElementsByClassName("dropdown-menu")[0];
    var hoge1 = whole_hoge.firstElementChild;
    var clone_hoge1 = hoge1.cloneNode(true);
    clone_hoge1.firstElementChild.innerText = text;
    whole_hoge.appendChild(clone_hoge1);
}