Open-vocabulary 3D Instance Segmentation methods (OV-3DIS) have recently demonstrated their generalization ability to unseen objects. However, these methods still depend on predefined class names during inference, restricting agents' autonomy. To mitigate this constraint, we propose a novel problem termed Open-Ended 3D Instance Segmentation (OE-3DIS), which eliminates the necessity for predefined class names during testing. We present a comprehensive set of strong baselines inspired by OV-3DIS methodologies, utilizing 2D Multimodal Large Language Models. In addition, we introduce a novel token aggregation strategy that effectively fuses information from multi-view images. To evaluate the performance of our OE-3DIS system, we benchmark both the proposed baselines and our method on two widely used indoor datasets: ScanNet200 and ScanNet++. Our approach achieves substantial performance gains over the baselines on both datasets. Notably, even without access to ground-truth object class names during inference, our method outperforms Open3DIS, the current state-of-the-art in OV-3DIS. Source code available at: https://github.com/PhucNDA/OE-3DIS.