How about drawing on the etymology/history of threes for a unique name?
From Wikipedia:
Quote:
The word "Trinity" comes from "Trinitas", a Latin abstract noun that means "three-ness," "the property of occurring three at once" or "three are one." The Greek term used for the Christian Trinity, "Τριάς" ("Trias," gen. "Triados") means "a set of three" or "the number three,"[3] and has given the English word triad.
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You could call each other "trinitas," "triune," or one of the above-quoted things from Wiki. You guys were English majors, right?... plenty of fodder there.
All hail the Triumvirate!
Or maybe more colloquially, "my better third?"
EDIT: Okay, that's more than a little weird. I was looking up etymologies and writing my post while ubertuber beat me to the punch. Guess that means it's a good idea, eh?