Terahertz (THz) communication has a large available bandwidth, which is expected to be deployed in future communication networks. As THz wave suffers from severe propagation loss in wireless transmission, we consider a THz near-field scenario where a base station (BS) is equipped with a large-scale antenna array with a low-cost hybrid beamforming architecture to serve mobile users nearby. However, the large-scale array and the user mobility incur difficulty in channel estimation. To tackle this issue, we propose a near-field beam training scheme that can align a beam to the user in a fast way by searching the codebook. Specifically, the BS employs a uniform circular array (UCA), and the radiation pattern of the beams in our proposed codebook appears as ellipsoids. To cover the serving zone with the minimum codebook size, we develop a near-field codebook by tangent arrangement approach (TAA). To reduce the time overhead, we leverage the hybrid beamforming architecture to realize multi-beam training concurrently since each RF chain can enable a codeword whose element has a constant magnitude. Numerical results validate that our proposed UCA near-field codebook achieves less time cost while achieving a comparable coverage performance compared to the conventional near-field codebook.