Is there a way to edit non-custom term attributes?

There’s a filter for taxonomy labels, taxonomy_labels_{$taxonomy} (the {$taxonomy} should be replaced with your custom taxonomy name) that allows you to filter pretty much all of it.

Example:

// Assuming your custom taxonomy is named 'faq_category'. Adjust as needed.
add_filter( 'taxonomy_labels_faq_category', 'wpse626542_taxonomy_labels' );
/**
 * Filters the taxonomy labels.
 *
 * @param  object $labels The taxonomy labels.
 * @return object         The filtered labels.
 */
function wpse426542_taxonomy_labels( $labels ) {
    // Changes the label on the Name field.
    $labels->name_field_description = __( 'My Custom Name Description', 'my-plugin' );
    // Change any other labels you want, and then...
    return $labels;
} 

A full list of the labels can be found in the get_taxonomy_labels() docs.