I'm using hook_block to create a block with the name of the custom module I'm creating.
I'm not being able to create a block without using myModuleName_block.
Do I need to do different modules for every different block I want to create?
You can make several blocks with hook_block, just use the $delta.
function hook_block($op = 'list', $delta = 0, $edit = array()) {
  switch ($op) {
    case 'list':
      $blocks[0]['info'] = t('Block 1');
      $blocks[1]['info'] = t('Block 2');
      return $blocks;
    case 'configure':
      if ($delta == 0) {
        // Block 1
      }
      else if ($delta == 1) {
        // Block 1
      }
 ....
}
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