The Melancholia of Departure was one of the smaller, vacuum-only shuttles carried aboard its mothership, the lighthuggerNostalgia for Infinity.
It was used by Ilia Volyova and fellow crew members for ferrying supplies and passengers between the lighthugger and the carousels of the Rust Belt in Yellowstone orbit.
The small ship's name is an obvious variation on the "theme naming" seen in the name of its mothership.
The spherical design of the shuttle, aside from being generally very practical in a vacuum environment, bears a striking similarity to the Aries Ib class shuttles of the Space odyssey series, authored by Arthur C. Clarke and first adapted to film by Stanley Kubrick. Alastair Reynolds is a self-confessed old fan of Clarke's body of work, so the chosen shape might also be a bit of a nod.
References
See also
Lighthugger spherical shuttle - The type of vacuum-only shuttle the Melancholia belonged to.