The arbiters are named after the floor they work on in Latin. Their bars' names translate to their floor numbers. Ginti works in Viginti on floor Viginti (20). Decim works in Quindecim on floor Quindecim (15).
Decim ' name may be a nod to one of the Roman gods of Fate, Decima. She measured the thread of life, which may reference the threads Decim uses to restrain people.