The table you want to change is cms_cpg_pictures. This is the table that contains all of the individual picture information. If you browse that table, you will find a filepath column that contains the path to the picture, minus the filename. You will want to update those columns with a query for each album, like this:
| PHP: |
update cms_cpg_pictures set filepath = 'modules/coppermine/albums/new_album_name_goes_here/' where filepath = 'modules/coppermine/albums/old_album_name_goes_here/'
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Of course, back your database up first. I would suggest running the query on one album first to test it. After the qurey, rename the folder in modules/coppermine/albums to your new_album_name_goes_here value.