Find following code at catalog/view/theme/YOUR_THEME_NAME/product/category.tpl
<h2><?php echo $heading_title; ?></h2>
<?php if ($thumb || $description) { ?>
<div class="row">
<?php if ($thumb) { ?>
<div class="col-sm-2">
<img src="<?php echo $thumb; ?>" alt="<?php echo $heading_title; ?>" title="<?php echo $heading_title; ?>" class="img-thumbnail" />
</div>
<?php } ?>
<?php if ($description) { ?>
<div class="col-sm-10"><?php echo $description; ?></div>
<?php } ?>
</div>
<hr>
<?php } ?>
In the above code heading title (or category name) is shown and checks whether category thumb image or description of that category is inserted or not. If only they are inserted then they are shown.
I have twisted to get your requirement,
Now replace with following code:
<div class="row">
<?php if ($thumb) { ?>
<div class="col-sm-2">
<img src="<?php echo $thumb; ?>" alt="<?php echo $heading_title; ?>" title="<?php echo $heading_title; ?>" class="img-thumbnail" />
</div>
<?php }else{ ?>
<h2><?php echo $heading_title; ?></h2>
<?php } ?>
<?php if ($description) { ?>
<div class="col-sm-10"><?php echo $description; ?></div>
<?php } ?>
</div>
<hr>
So now as per the above code, category image is shown if there is category image nor category name is shown. If description is inserted then description is shown.