Worldbuilding

You can get them to spit out a list of name suggestions that follow a theme pretty easily. Modify them as you see fit.

I have a city created by some outcasts, one of them had a passion for programming, so they created an AI with the intent of protecting the city from the dangerous beasts that lurked outside. Unfortunately, the AI created was intelligent enough, but misaligned with human values. It judged the humans as possible threats to itself and the city (as they knew how to turn it off), and expelled them forcefully outside the walls of the city, where they died.

It it's what we call ai in the current reality, aka llms then not much.

But if the were proper AI then I would use them like Babylon 5. Personal assistants.

True sapient AI is impossible in my current conworld. That hasn't stopped people from trying for it though. The Mindseekers were a sect of Neoshamanists who sought to create sapient life anew artificially rather than seek other sophonts among the stars like the Bright Way. In the early days they were regarded like alchemists, seekers of forbidden knowledge. And just like Terran alchemy blossomed into chemistry, the Mindseekers found themselves at the forefront of the digital revolution when electronics became economically feasible. While they never achieved their goal of creating conscious AI, they founded the field of computer science in the process, which in tern eventually allowed the Bright Way to advance rocketry to the point they could breach the atmosphere.

Are we talking about currently-as-it-exists "AI" (i.e., highly sophisticated pattern matching)? Then we pretty much already know the best uses - some data analyses for scientific purposes, leading to new discoveries or better predictive models. You can mix in some sci-fi flavor for it, but really the base use cases doesn't change. Just remember to have a human monitoring the whole mess.

...though honestly, I'd be interested to see a sci-fi space empire deploy AIs trained to be as disruptive and awful as possible into an enemy social space, then just sit back and watch the fireworks.

But if we're talking about fictional AI as it is popularly conceived (i.e., a near-human intelligence minimum) - Star Wars' droids, Star Trek's androids, BSG's Cylons, etc - well, now we're talking pure fiction, so what uses do you want to do with it?