Don't know why Mageplaza haven't still listed the composer name of their paid extensions. Look at the comment section of this tutorial: https://bit.ly/2Z9P7jC; you will see users asking for composer name, and still no solution is provided by them. Today I tried posting this solution as a comment in the aforementioned page, and each time my comment got deleted for reasons unknown to me. That's why I have decided to post this solution here.
The solution is very simple. Just download the extension, and look in the composer.json file. You will see a key/value pair entry as follows:
"name": "mageplaza/module-search"
Here module-search is the composer name of the paid extension Ajax Search for Magento 2.
NOTE: If you are installing Mageplaza extensions for the first time via composer, make sure to run the following command first:
$ composer config repositories.mageplaza composer https://repo.mageplaza.com