From your original post, it sounds like you have all your courses in one category. You'll need to find out the ID number of that category.
If you go to http://your.moodle.site/course on your site and then click on the category of interest you will see its ID number in the URL. It will contain /course/category.php?id=X where X is the category ID.
You should now be able to write a query to modify the shortname of courses directly under this category. If there are nested categorys it's going to be more complicated.
BACKUP YOUR DATABASE NOW in case you break anything. And make sure you know how to restore it if needed. In fact, do all this on a test server to prove that it works as I can't be held responsible for this breaking everything if it's in fact completely wrong
Seeing as you also mentioned phpmyadmin I'll assume you have a MySQL database.
Using phpmyadmin browse to your moodle database and find the course table (probably called mdl_course unless someone chose to use a non-default prefix in place of the standard mdl_).
So once your phpmyadmin shows you're at
localhost -> moodle -> mdl_course
To test it the first time add " LIMIT 1" without the double quotes to the end so that it will only modify the first record it finds as a test case. NOTE that the query contains both single quotes as well as backticks (backwards single quotes) and you'll need to get the right ones in the right place or MySQL will get confused and return an error. I'm not sure if these quote and backtick requirements are different for MySQL running on Windows or other platforms.
Of course if you wish to change the idnumber of the course rather than the shortname simply replace the two instances of shortname in the query with idnumber.
PLEASE: test first, backup first, have a perfect recovery plan when running queries directly on your database