Cross-view object correspondence, exemplified by the representative task of ego-exo object correspondence, aims to establish consistent associations of the same object across different viewpoints (e.g., egocentric and exocentric). This task poses significant challenges due to drastic viewpoint and appearance variations, making existing segmentation models, such as SAM2, difficult to apply directly. To address this, we present V2-SAM, a unified cross-view object correspondence framework that adapts SAM2 from single-view segmentation to cross-view correspondence through two complementary prompt generators. Specifically, the Cross-View Anchor Prompt Generator (V2-Anchor), built upon DINOv3 features, establishes geometry-aware correspondences and, for the first time, enables coordinate-based prompting for SAM2 in cross-view scenarios, while the Cross-View Visual Prompt Generator (V2-Visual) enhances appearance-guided cues via a novel visual prompt matcher that aligns ego-exo representations from both feature and structural perspectives. To effectively exploit the strengths of both prompts, we further adopt a multi-expert design and introduce a Post-hoc Cyclic Consistency Selector (PCCS) that adaptively selects the most reliable expert based on cyclic consistency. Extensive experiments validate the effectiveness of V2-SAM, achieving new state-of-the-art performance on Ego-Exo4D (ego-exo object correspondence), DAVIS-2017 (video object tracking), and HANDAL-X (robotic-ready cross-view correspondence).