To add to the loop (even if the information is not used in the loop):
<?php $categories = get_the_category();
$image=$categories[0]->slug;
$nom=$categories[0]->cat_name;?>
If it does not work:
<?php foreach((get_the_category()) as $category) {
var_dump($category);
$image=$category->slug;
$nom=$category->cat_name;
}?>
If a page category:
<?php $categories = get_category( get_query_var( 'cat' ) );
$image=$categories->slug;
$nom=$categories->cat_name; ?>
Then reuse the information in the variables, it remains only display:
<?php echo $nom;?>
Want to see the information in the table? Very well!
<?php var_dump($categories); ?>