JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<select name="name0" id="myselect">
<option value="1" data-name="name1">Опция 1</option>
<option value="2" data-name="name2">Опция 2</option>
<option value="3" data-name="name3">Опция 3</option>
</select>

JavaScript

$("#myselect").on('change', function() {
	var selectedOption = $("option:selected", $(this));
	$(this).attr("name", selectedOption.data("name"));
  alert($(this).attr("name"));
});