Background information Edit
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) Bonchune speculates it was an internal name used by the art department or an arbitrary choice by the model builder. Additional views of the design can be found at the Drex Files(X).
Regardless of its origins, the name stuck and was by the franchise elevated to "semi-official" status when the ship received its own outing in the British partwork publication Star Trek: The Official Starships Collection as issue 124 in 2018, though it did not receive an entry in the fourth edition of the Star Trek Encyclopedia.
This ship was 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. Because the opening titles were presented vaguely chronologically, this would place the ship between the late-21st century, when the first Lunar colonies were founded, and the mid-22nd century, when Enterprise was launched.
The mirror universe counterpart was seen in the "mirror" title sequence for "In a Mirror, Darkly" and "In a Mirror, Darkly, Part II". Unlike the regular universe version, the mirror ship is actually seen firing its weapons as it flies over Luna.