Temporal Graph Networks (TGNs) have demonstrated their remarkable performance in modeling temporal interaction graphs. These works can generate temporal node representations by encoding the surrounding neighborhoods for the target node. However, an inherent limitation of existing TGNs is their reliance onfixed, hand-crafted rules for neighborhood encoding, overlooking the necessity for an adaptive and learnable neighborhood that can accommodate both personalization and temporal evolution across different timestamps. In this paper, we aim to enhance existing TGNs by introducing anadaptive neighborhood encoding mechanism. We present SEAN (Selective Encoding for Adaptive Neighborhood), a flexible plug-and-play model that can be seamlessly integrated with existing TGNs, effectively boosting their performance. To achieve this, we decompose the adaptive neighborhood encoding process into two phases: (i) representative neighbor selection, and (ii) temporal-aware neighborhood information aggregation. Specifically, we propose the Representative Neighbor Selector component, which automatically pinpoints the most important neighbors for the target node. It offers a tailored understanding of each node's unique surrounding context, facilitating personalization. Subsequently, we propose a Temporal-aware Aggregator, which synthesizes neighborhood aggregation by selectively determining the utilization of aggregation routes and decaying the outdated information, allowing our model to adaptively leverage both the contextually significant and current information during aggregation. We conduct extensive experiments by integrating SEAN into three representative TGNs, evaluating their performance on four public datasets and one financial benchmark dataset introduced in this paper. The results demonstrate that SEAN consistently leads to performance improvements across all models, achieving SOTA performance and exceptional robustness.