Set default (auto) slug prefix for Tags

You can use the created_term or the created_{taxonomy} hooks which are fired just after a taxonomy term is created (the second only if it matches the taxonomy).

The following will only alter terms in the taxonomy ‘my-taxonomy’. (I believe for the default tags, taxonomy should be ‘post_tag’).

add_action('created_term', 'my_add_prefix_to_term', 10, 3);
function my_add_prefix_to_term( $term_id,$tt_id,$taxonomy ) {
    if( $taxonomy == 'my-taxonomy'){
        $term = get_term( $term_id, $taxonomy );
        $args = array('slug'=>'my-prefix-'.$term->slug);
        wp_update_term( $term_id,$taxonomy, $args );
    }
}

Note: From the Codex:

It should also be noted that if you set ‘slug’ and it isn’t unique then a WP_Error will be passed back

This shouldn’t be a problem if you use this function before any terms are created, because prefixing the same string to unique slugs preserves uniquness.