Vision-language models (VLMs) such as CLIP exhibit strong Out-of-distribution (OOD) detection capabilities by aligning visual and textual representations. Recent CLIP-based test-time adaptation methods further improve detection performance by incorporating external OOD labels. However, such labels are finite and fixed, while the real OOD semantic space is inherently open-ended. Consequently, fixed labels fail to represent the diverse and evolving OOD semantics encountered in test streams. To address this limitation, we introduce Test-time Textual Learning (TTL), a framework that dynamically learns OOD textual semantics from unlabeled test streams, without relying on external OOD labels. TTL updates learnable prompts using pseudo-labeled test samples to capture emerging OOD knowledge. To suppress noise introduced by pseudo-labels, we introduce an OOD knowledge purification strategy that selects reliable OOD samples for adaptation while suppressing noise. In addition, TTL maintains an OOD Textual Knowledge Bank that stores high-quality textual features, providing stable score calibration across batches. Extensive experiments on two standard benchmarks with nine OOD datasets demonstrate that TTL consistently achieves state-of-the-art performance, highlighting the value of textual adaptation for robust test-time OOD detection. Our code is available at https://github.com/figec/TTL.