As per my understanding,
Step 1: Get the name/Value
var name = $('#dropdownId' option:selected).val();
Step 2: Append it into text box.
$('#textboxId').val(name);
Step 3:
Keep the above code (step 2) inside document.Ready(function)/On load/Next button click in case of Wizard.
Please accept the solution if this helps otherwise give exact scenario so that we can find some solution.