Loop through entry titles in a select field
The issue is you don't have a variable named input. I changed the code a little by included a variable named value. To make sure the proper option is selected you would need to pass back to the template a url param name with the currently selected option value.  If there is a param and it has a value it will add that value to the variable value if not value will be blank.

&lt;label&gt;Position Applying For&lt;/label&gt;
{% set value = craft.request.getParam("name")?? "" %}
&lt;select name="{{ positionApplyingFor.handle }}"&gt;
    {% for entry in craft.entries.section('careers') %}
        &lt;option value="{{ entry.title }}" {% if value == entry.title %}selected{% endif %}&gt;
            {{ entry.title }}
        &lt;/option&gt;
    {% endfor %}
&lt;/select&gt;