What is the proper way to use add_rewrite_rule to remove the (question mark)?

Question

I have a page called "People" with a custom template that takes in a variable called name:

example.com/people/?name=FirstLast

What I want is this:

example.com/people/FristLast

I know I need to use the add_rewrite_rule and add_rewrite_tag calls but I'm not sure how to achieve my desired result. I've tried this but I get a php error:

add_rewrite_rule('^people/([^/]*)/?','index.php?name=$matches[1]','top');
add_rewrite_tag('%name%','([^&]+)');

The error I get is: "Fatal error: Call to a member function add_rule() on a non-object"

I think I'm on the right path. I'm very knowledgeable with WP but this is my first attempt to the rewrite rule.

Thanks!

----- EDIT ----- I've updated the code. I no longer get an error but nothing "happens"

function rewrite_rule_people() {
    global $wp_rewrite;
    add_rewrite_tag('%name%','([^/]*)');
    add_rewrite_rule('^people/([^/]*)','index.php?page_id=42602&name=$matches[1]','top');
    $wp_rewrite->flush_rules();
}
add_action( 'init', 'rewrite_rule_people' );

going to /people/?name=JohnSmith doesn't change the url to /people/JohnSmith

Answer 1

You need to use your page id of "People" page. If i assume it is 12 then this will do,

add_rewrite_rule('^people/([^/]*)/?','index.php?page_id=12&name=$matches[1]','top');