NamesGenerator.ai - use WP plugin to generate names. How to use it to generate premium domains?

The AI Enabler Plugin is an innovative tool for WordPress that makes your website more interactive and engaging by using AI. With this plugin, you can easily create smart forms that respond to users in real-time, making your site more dynamic and user-friendly.

Key Features​

AI-Driven Forms: The main feature of the AI Enabler Plugin is its AI-powered forms. These forms are not only free to use but also simple to set up. They connect directly with ChatGPT, allowing your website to offer intelligent and relevant answers to user questions.

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I have checked where plugin is live, and here it is on NamesGenerator.ai

Using the AI Enabler Plugin for WordPress to generate premium domain names and check their availability would likely require additional functionality beyond what the plugin offers out of the box. While the AI Enabler Plugin is designed to create interactive forms powered by ChatGPT, it does not inherently include features for domain name generation or availability checking.

So I have find Free plugin here https://wordpress.org/plugins/ai-enabler/
I'm not sure what Domain Registrar have free API, so I can setup it in simple way on WordPress. Maybe someone here know, or even maybe there are get ready solutions?