JSFiddle - React, Tailwind, and code Playground

HTML

<header>
  <div id="banner">
    <!-- main content -->
  </div>
  <div class="pheader">
    <div class="user-panel">
      <div id="hey-user" class="d2c-user-panel">
        <img src="http://www.fnordware.com/superpng/pnggrad8rgb.png" class="userimg">
        <!-- Hide This -->
        <span class="caret" id="down-arrow"></span>
        <span class="hey-user d2c-header-username"><b>Hello</span>
      </div>
</header>

CSS

#banner + .pheader img {
  display: none;
}

#banner + .pheader span {
  display: none;
}