Dynamic Stamp with dropdown

Take a look at this tutorial: https://acrobatusers.com/tutorials/print/dynamic_stamp_secrets

For more complex user interfaces (e.g. a dropdown control), you will need a custom dialog, which adds another level of complexity to your stamp project. Take  look at the sample code in the Acrobat JavaScript API documentation: Acrobat DC SDK Documentation - App.execDialog() 

The stamp itself doesn't really need a dropdown, but you can create a custom dialog that includes a dropdown when prompting the user to enter some data to include in the stamp. If you do a Google search with terms like "Acrobat dynamic stamp custom dialog JavaScript dropdown" you should find enough examples to get you started.