You can add a snippet of text to your launcher button to make it look similar to this:
To set this up, first go to "Settings > Translation" and enter the text you'd like displayed in the "Launcher" section.
Next, go to "Settings > Account Settings > Advanced Settings > Widget" and set "Show Launcher Text?" to "Yes".
That's it, now you will see the text snippet next to your launcher button on your website. If you'd like to style the text container using CSS, you can do so with your site CSS - note that adding styles to the custom CSS portion of Glow will not affect your launcher - only CSS on your theme can change the launcher.
To style your launcher text will css, you'll want to use the selector #loyalty_callout_container
Here is an example: