Is there a filter hook that I can use to change how taxonomy term names are displayed?

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;
} );