JSFiddle - React, Tailwind, and code Playground

HTML

<div style="position:absolute;top:0;right:0;padding:4px;">
    <div style="position: relative;">
        <div id="logout_button">
            Dynamic Name
        </div>
        <div id="logout_panel">
            <div style="position: relative;">
               <a href="?page=logout">Logout</a>
            </div>
         </div>
     </div>
</div>

CSS

#logout_button{
	padding: 0 5px 0 5px;
	background-image: url("../img/bg-menu.png");
	border: 1px solid #fff;
	border-radius: 3px;
	line-height: 30px;
	position: absolute;
	top: 30px;
	right: 5px;
	z-index:1;
    display: inline-block;
}

#logout_panel{
	position: absolute;
	right: 5px;
	top: 60px;
	display: none;
	background-color: #e9e9e9;
	width: 300px;
	height: 140px;
	border: 1px solid #fff;
	border-radius: 3px 0 3px 3px;
	z-index: 1;
}

JavaScript

$(document).ready(function(){
  $("#logout_button").click(function(){
    $("#logout_panel").toggle();
  });
});