The theme contains no feature for this, and so this will be a customization you’ll need to make from your Child theme.
This HTML markup is controlled from the function called “alyeska_blog_meta” found in /includes/theme-functions.php of the theme. To customize this function, you can copy it to your Child theme. — There you’ll find the anchor tag wrapping the author’s name you can remove.
How to edit theme functions from your Child theme: http://dev.themeblvd.com/tutorial/editing-framework-functions/