Insert Info In Input Boxes -> Select Fields

I am working on a project that requires me to insert info in input boxes (2 input boxes to be specific, firstname, and last name are the two) and transfer that info into a <select> field when the button is clicked. So, let's say in the first input box which is first name I type Tom and in the second input box which is last name I type Smith. When I click the button I want the first and last name to appear in the select field as an option. Now, i tried researching about adding/removing options for the select field, but nothing on getting info from input boxes to put it as an option in <select>.