Do AI creations in which my name is mentioned in the prompt (for example: a 'artist' style image) infringe my copyright?
Basically, your 'style' is not protected under copyright law. In fact, artistic movements or styles are not covered by copyright protection because that could inhibit artistic development. For example, imagine if one person could have appropriated the rights to 'cubism': this would have led to undesirable situations. So someone may create something in your style, whether with the help of AI or not. However, training the AI with your work may potentially infringe your copyright.
Moreover, an AI production that incorporates so-called "copyrighted traits" may also potentially infringe. This may be the case if, for example, not only the style is imitated, but really certain copyrighted characters are copied. The assessment of this depends very much on the circumstances of the case, and should be reviewed individually for each case.