The dynamic filter "term_{$field}"
is probably what you’re looking for, where the field is “name.”
One approach is to have an array of names and their pseudonyms, then do a check-and-return on them so they’ll display the replacement.
add_filter( 'term_name', function( $value ) {
$terms = [
'old' => 'new',
];
// basic example check, loop through an array for real
if ( 'old' === $value ) {
return $terms['old'];
}
return $value;
} );