I think they call that focus "AI Engineer".
Edit: just realized you might also be thinking of "MLOps". See end of comment.
It's what I have been doing for the last two years but I refer to it as "software engineer with a recent focus on generative AI".
I also think AI Integration Engineer is good but I have only really seen AI Engineer.
The thing is, up until a few years ago, doing useful things with AI generally did require something more like machine learning knowledge.
But now that we have general purpose models like gpt-4o, Claude 3.5, LlaVA, etc., you can just do an API call and in a day or two have a more functional system than what a machine learning engineer may have spent months training a custom model on previously.
So that somewhat explains the confusion. I think it's best to just honest. Most applications actually don't need "real" ML knowledge or custom neural network architectures or training a model from scratch.
I do think that ML is a good field to be in if you have the patience to learn the math and about neural networks etc. But I think that is not what you are talking about. And the architectures and models are very general purpose so as I said you can work on many applications of ML now without having that background.
Go to the Anthropic or OpenAI documentation and copy paste their examples and try inserting some customization into the system message using an f-string.
I think MLOps is also a thing. Go to HuggingFace and RunPod and practice deploying models with Python. Also find some tutorials on LLM pre-training, fine-tuning, and evaluations. Check out Predibase.
A big thing right now I believe is Diffusion Transformers. If you can find some article explaining how to run a training job for that, you may be able to help people.
If you want to "cheat", check out replicate.com. cog could be useful for self hosting ML models outside of replicate.com also.