The name disambiguation task partitions a collection of records pertaining to a given name, such that there is a one-to-one correspondence between the partitions and a group of people, all sharing that given name. Most existing solutions for this task are proposed for static data. However, more realistic scenarios stipulate emergence of records in a streaming fashion where records may belong to known as well as unknown persons all sharing the same name. This requires a flexible name disambiguation algorithm that can not only classify records of known persons represented in the train- ing data by their existing records but can also identify records of new ambiguous persons with no existing records included in the initial training dataset. Toward achieving this objective, in this paper we propose a Bayesian non-exhaustive classification frame- work for solving online name disambiguation. In particular, we present a Dirichlet Process Gaussian Mixture Model (DPGMM) as a core engine for online name disambiguation task. Meanwhile, two online inference algorithms, namely one-pass Gibbs sampler and Sequential Importance Sampling with Resampling (also known as particle filtering), are proposed to simultaneously perform online classification and new class discovery. As a case study we consider bibliographic data in a temporal stream format and disambiguate authors by partitioning their papers into homogeneous groups.Our experimental results demonstrate that the proposed method is significantly better than existing methods for performing online name disambiguation task. We also propose an interactive version of our online name disambiguation method designed to leverage user feedback to improve prediction accuracy.