How to Print out Category Name and Sub Category Name on category.php

the category id in a category archive is:
get_query_var('cat')

https://codex.www.ads-software.com/Function_Reference/get_category_parents
the code could be, for example:

<?php echo get_category_parents(get_query_var('cat'), TRUE, ' > '); ?>

if you want this only for sub-cats, you need to wrap it into a conditional statement, such as if( get_category(get_query_var('cat'))->parent ) { ... }

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not sure for what purpose you need the full urls and for what levels;
here some links to resources:
https://codex.www.ads-software.com/Function_Reference/get_ancestors
https://codex.www.ads-software.com/Function_Reference/get_category_link
https://codex.www.ads-software.com/Function_Reference/get_category