This ship is seen flying above Luna in the opening titles of Star Trek: Enterprise as Connor Trinneer's credit plays, right after a scene of the Phoenix in 2063 and before a scene of Enterprise in 2151. This suggests that this ship was in use sometime between the late-21st century, when the first Luna colonies were founded, (DS9: "Valiant") and the mid-22nd century, when Enterprise was launched.
Additional views of the design can be found at the Drex Fileswbm. In his blog, Doug Drexler names the ship as the SS Emmette. The name comes from the CGI model files the ship was saved as by the art department. The name was not invented by John Eaves,  Robert Bonchune, or Doug Drexler. [X]wbm Bonchune speculates it was an internal name used by the art department or an arbitrary choice by the model builder.