rename custom taxonomy

functions.php

add_action( 'init', 'my_modify_taxonomy', 11 );

function my_modify_taxonomy() {

    // get the arguments of the already-registered taxonomy
    $my_category_args = get_taxonomy( 'project_category' );

    // make changes
    $my_category_args->rewrite['slug'] = 'genre';

    // re-register the taxonomy
    register_taxonomy( 'project_category', 'author', (array) $my_category_args );
}