For every taxonomy you have to choose a unique name, which is used in the database. so so your new e.g. players_region
.
<?php
add_action( 'init', 'build_taxonomies' );
function build_taxonomies() {
register_taxonomy(
'players_team', // Unique name.
'player', // Post type.
array(
'hierarchical' => true,
'label' => 'Players Team',
'query_var' => true,
'rewrite' => true,
)
);
register_taxonomy(
'players_region',
'player',
array(
'hierarchical' => true,
'label' => 'Players Region',
'query_var' => true,
'rewrite' => true,
)
);
}