Make sort dropdown keep property
In short, you need to set the selected attribute on the option element based on the sort order.

So, if the sort order is title asc, then that option would have the selected (selected="selected") attribute set on it.

I took the liberty to refactor your code to render sort options dynamically and make the selected sort order sticky by comparing the current option being iterated over, against the selected sort option.

{% set sortOptions = [
    {
        label: 'New - Old',
        value: 'postDate asc'
    },
    {
        label: 'Name Z - A',
        value: 'title desc'
    },
    {
        label: 'Name A - Z',
        value: 'title asc'
    },
] %}

{% set selectedSortOption = craft.request.getParam('order', 'title asc') %}

{% for category in craft.categories.group('university').order(selectedSortOption) %}
    {{ category.title }}
{% endfor %}

&lt;select class="sort-web w-select" data-name="Sort" id="sortQuery" name="Sort"&gt;
    {% for sortOption in sortOptions %}
        &lt;option value="{{ sortOption.value }}" {{ sortOption.value == selectedSortOption ? 'selected' }}&gt;
            {{ sortOption.label }}
        &lt;/option&gt;
    {% endfor %}
&lt;/select&gt;


Feel free to follow up if you have any questions.