Two different menus for two different locations?

You most probably used the theme location part wrongly. Here is an example of how it should be done

Follow the comments in code for explanation 🙂

add_filter( 'wp_nav_menu_args', function ( $args ) 
{
    if (    is_page( 2 ) //Only target page 2 
         && $args['theme_location'] === 'primary' ) { // Check and only target the primary menu
    ) {
        $args['menu'] = 'Menu for Profile';
    }
    return $args;
});