use a single nonce in three different nonce field

You can pass multiple nonces with wp_localize_script() by just including them as separate properties in the ajax_login_object object.

wp_localize_script( 'ajax-login-script', 'ajax_login_object', array(
        'ajax_url'                 => admin_url( 'admin-ajax.php' ),
        'login_nonce_token'        => wp_create_nonce( 'login_nonce' ),
        'register_nonce_token'     => wp_create_nonce( 'register_nonce' ),
        'lostpassword_nonce_token' => wp_create_nonce( 'lostpassword_nonce' ),
) );

Then in your JS, use the correct one from your localize object as the value for each request, and use the same _ajax_nonce name for the field name.

data: {
    'action': 'ajaxlogin',
    '_ajax_nonce': ajax_login_object.login_nonce_token,

data: {
    'action': 'ajaxregister',
    '_ajax_nonce': ajax_login_object.register_nonce_token,

data: {
    'action': 'ajaxlostpassword',
    '_ajax_nonce': ajax_login_object.lostpassword_nonce_token,

Then in your AJAX handler, use the names you gave them when creating them with wp_create_nonce() for the first argument, and the field name as the second argument:

check_ajax_referer( 'login_nonce', '_ajax_nonce' );

check_ajax_referer( 'register_nonce', '_ajax_nonce' );

check_ajax_referer( 'lostpassword_nonce', '_ajax_nonce' );

The second argument needs to be the field name we used in JavaScript, which is _ajax_nonce, but this is the default value (which is why we used it), so we can leave it out, if we want:

check_ajax_referer( 'login_nonce' );

check_ajax_referer( 'register_nonce' );

check_ajax_referer( 'lostpassword_nonce' );