Name ambiguity is a prevalent problem in digital library domain where mapping of bibliographic records to authors is a major issue. The unprecedented growth of the bibliographic records and absence of unique identifiers are further exacerbating the problem. Specifically, name ambiguity affects various bibliometric analysis tasks that include record management as well as scientific assessment of the authors thereby necessitating the name disambiguation. The name disambiguation task is to assign the records, possibly with the ambiguous authorship, to corresponding authors. While existing techniques are good at extracting abstract features from set of records with a common author name that can be subsequently used for clustering the records based on unique author identities, however, such techniques usually perform poorly in disambiguating isolated individual record entries that arrive continuously. Disambiguation of only newly arrived records, rather than the whole records of the digital library is challenging, however, computationally rewarding and thus, not only preferable but becoming the necessity due to tremendous growth in the number of bibliographic records with the time, which is likely to continue. In this regard, we propose an online author name disambiguation approach for evolving digital library. Our approach involves representation learning of records in an online manner in evolving (academic networks) digital library using dynamic graph embedding and clustering of latent representation of records. We show the use of our online name disambiguation method in batch setting (for static or initial records of digital library) and incremental setting (for new records of digital library). Significant improvement, over existing state-of-the-art methods in terms of various evaluation metrics, has been observed which indicates the effectiveness of the proposed approach.