According to https://developer.ninjaforms.com/codex/changing-field-values/ you need to add .trigger( 'change' )
when changing Ninfa Forms field values programmatically.
This should work:
if(jQuery('#broker-list').length) { //checks if the list exists
jQuery(document).on( 'nfFormReady', function( e, layoutView ) {
var broker_name = "";
jQuery(document).on("click", ".broker" , function() {
broker_name = jQuery('.broker__name', this).text();
console.log(broker_name); // this works perfectly
if(jQuery('#nf-field-33').length) {
jQuery(this).val(broker_name).trigger( 'change' );
}
if(jQuery('#nf-field-34').length) {
jQuery(this).val(broker_name).trigger( 'change' );
}
});
});
}