Positron emission tomography/computed tomography (PET/CT) is essential in oncology, yet the rapid expansion of scanners has outpaced the availability of trained specialists, making automated PET/CT report generation (PETRG) increasingly important for reducing clinical workload. Compared with structural imaging (e.g., X-ray, CT, and MRI), functional PET poses distinct challenges: metabolic patterns vary with tracer physiology, and whole-body 3D contextual information is required rather than local-region interpretation. To advance PETRG, we propose PETRG-3D, an end-to-end 3D dual-branch framework that separately encodes PET and CT volumes and incorporates style-adaptive prompts to mitigate inter-hospital variability in reporting practices. We construct PETRG-Lym, a multi-center lymphoma dataset collected from four hospitals (824 reports w/ 245,509 paired PET/CT slices), and construct AutoPET-RG-Lym, a publicly accessible PETRG benchmark derived from open imaging data but equipped with new expert-written, clinically validated reports (135 cases). To assess clinical utility, we introduce PETRG-Score, a lymphoma-specific evaluation protocol that jointly measures metabolic and structural findings across curated anatomical regions. Experiments show that PETRG-3D substantially outperforms existing methods on both natural language metrics (e.g., +31.49\% ROUGE-L) and clinical efficacy metrics (e.g., +8.18\% PET-All), highlighting the benefits of volumetric dual-modality modeling and style-aware prompting. Overall, this work establishes a foundation for future PET/CT-specific models emphasizing disease-aware reasoning and clinically reliable evaluation. Codes, models, and AutoPET-RG-Lym will be released.