Hi cuthza. Depending on which blog post layout you’re using, and whether you want to change the featured posts, you would copy content.php, content-standard.php or content-featured.php to your child theme. Then find this section:
<div class="post-meta group">
<p class="post-category"><?php the_category(' / '); ?></p>
<?php get_template_part('parts/post-list-author-date'); ?>
</div><!--/.post-meta-->
and change it to this, making the category line a comment (just in case you want it later) and adding the author link line:
<div class="post-meta group">
<!-- <p class="post-category"><?php the_category(' / '); ?></p> -->
<span class="fn"><?php the_author_posts_link(); ?></span>
<?php get_template_part('parts/post-list-author-date'); ?>
</div><!--/.post-meta-->
Then add this in you child theme style.css file:
.post-meta .fn{
float: left;
margin-right: 10px;
}