How to change a user role after registering in multisite?

I understand that your question is about to establish a default role for a site, such as ‘contributor’ or ‘author’, but also when the site does not exists yet.

I found a code snippet that changes the role when the user creates a blog:

function user_role_to_new_blog($blog_id, $user_id) {
    add_user_to_blog($blog_id, $user_id, 'author' );
}

add_action( 'wpmu_new_blog', 'user_role_to_new_blog', 10, 2 );

The original link is here.

If you want a default role for the users of the already created site then you go to Network Admin -> Sites, select ‘Edit’ in a site, then ‘Settings’ tab and search for a ‘default role’ setting, you’ll see a text for the role and you can change it according to your preferences. After that, save the changes.

Cheers