I use a very expansive definition of procedural generation around here. As such, I’m perfectly comfortable calling things like that AI tools.
AI has a definitional problem, in that once an AI problem is solved we often stop calling it AI. So simple name generators are, in my mind, perfectly reasonable to call AI tools. They’re a tool that uses AI to help you do something.
I feel like a lot of times when people ask about “AI” they’re picturing something like the robots in R.U.R. or the various computer characters in films and television. Sometimes people use terms like “Artificial General Intelligence” or “Strong AI” or “Real AI” to distinguish an-AI-as-a-person-level-intellect from the AI-as-just-a-bunch-of-math. I don’t find this particularly useful, given that we don’t have anything like that at the moment, and that even passing the Turing test is of limited utility (for both us as humans and the machine in itself).
The AI scholar Max Kreminski has been talking about the idea of xenopomorphism: rejecting both anthropomorphic & purely mechanistic ways of looking at AI. AI as companion species and household gods, rather than superhuman beings or calculators.
Humans are tool-using. While name generators are not terribly computationally intensive, they are still a tool that gives humans an ability that we wouldn’t have without it: Humans are really, really bad at randomization. Anything that prompts us to move out of our rut is useful as a creative tool. There’s a long history of authors and artists using various devices to help put them in a certain mood or to inspire ideas.
You can always make a better name generator, depending on what your goal is, but even a basic name generator can be a useful procedural generation tool.