Generative AI (GenAI) presents challenges in attributing synthesized content to its original training data, particularly for artists whose styles are replicated by these models. We introduce CustomMark, a novel technique for customizing pre-trained text-to-image GenAI models to enable attribution. With CustomMark, text prompts can be modified to embed a watermark in generated images, linking them to training concepts such as an artist's style, specific objects, or the GenAI model itself. Our approach supports sequential customization, allowing new concepts to be attributed efficiently and scalably without retraining from scratch. We demonstrate that CustomMark can robustly watermark hundreds of individual concepts and support multiple attributions within a single image while preserving high visual quality of the generation.