Add-PSSnapIn Microsoft.SharePoint.PowerShell

$containerCode = @"
<div id='webTitleContainer' class='ms-core-brandingText'></div>
<script type='text/javascript'>
(function() {
    // Set a default title to use if we cannot retrieve one.
    var defaultTitle = '';

    // Ensure that both the DOM and the Object Model are ready for us
    document.addEventListener('DOMContentLoaded', function() {
        EnsureScriptFunc('sp.js', 'SP.ClientContext', function() {
            // Get and load a reference to the root web of the current site collection.
            var context = new SP.ClientContext.get_current();
            var web = context.get_web();
            context.load(web);

            // Query SharePoint for the current sites title and URL
            context.executeQueryAsync(function(){
                 var title = web.get_title();
                 var url = web.get_url();

                 // If the current site isn't the homepage then add the title and link of the current site to the top bar
                 if(title != 'SharePoint Home' && title != 'Home') {
                    document.getElementById('titleContainer').innerHTML = title;
                    document.getElementById('currentSiteUrl').href = url;
                    document.getElementById('titleDivider').style.display = 'inline'
                    document.getElementById('titleContainer').style.display = 'inline';
                 }
              },
              function(sender,args){
                 console.log(args.get_message());
              }
            );
        });
    });

    function titleBarRenamer() {
        // Get and load a reference to the root web of the current site collection.
        var context = new SP.ClientContext.get_current();
        var web = context.get_web();
        context.load(web);
        context.executeQueryAsync(function(){
            // Query for the current site title
             var title = web.get_title();
             var url = web.get_url();

             if(title != 'SharePoint Home' && title != 'Home') {
                document.getElementById('titleContainer').innerHTML = title;
                document.getElementById('currentSiteUrl').href = url;
                document.getElementById('titleDivider').style.display = 'inline'
                document.getElementById('titleContainer').style.display = 'inline';
             }
          },
          function(sender,args){
             console.log(args.get_message());
          }
        );
    }
})();
</script>
"@

$webApp = Get-SPWebApplication -Identity "*SharePointUrl*"
$webApp.SuiteBarBrandingElementHtml = "<div class='ms-core-brandingText'><a href='*SharePointUrl*' style='color:#fff;'><img style='margin-bottom:-1px; padding-right:5px;' src='*fullLinkToImage*'>SharePoint Home</a><span id='titleDivider' style='display:none;'> - </span><a id='currentSiteUrl' href='#' style='color:#fff;'><span id='titleContainer' style='display:none;'>$containerCode</span></a></div>"
$webApp.Update()