Two-dimensional regular string black hole in different gauges

This paper serves as an extended version of our previous letter arXiv:2212.03808 [hep-th]. In this paper, we investigate the non-perturbative and non-singular black hole solutions derived from complete $\alpha^{\prime}$ corrected Hohm-Zwiebach action in different gauges (coordinate systems). In addition to the results that we obtained in the previous letter, we present the following additional results in this paper: 1) The regular black hole solutions in different gauges can be mutually transformed. 2) The $\alpha^{\prime}$ corrections do not introduce any extra singularities beyond the event horizon. 3) The event horizon remains unaffected by the $\alpha^{\prime}$ corrections. The results of this paper provide valuable illustrations for further investigation of more complicated regular black hole solutions utilizing the complete $\alpha^{\prime}$ in the near future.