How can I add new options to a dropdown dynamically?

For instance, I'll be adding new group name, I want the group name to show on the existing group drop down?

I'm sorry, but I don't fully understand your question.
Do you want to dynamically add options to a dropdown?

If so, you can check our User Contributed Dropdown widget which provides this functionality. You can see a demo form here: http://form.jotformpro.com/form/43438068244962

Let us know if this would work for you.