I think the official (or at least accepted) names for three color factions are shards and wedges (ally colors being shards after Shards of Alara and enemy colors being wedges due to the wedge shape they make when connected on the back of a magic card.)
Shards are the three color groups that have three "Unbroken" colors in the WUBRG circle. Bant - GWU (White is Primary) Esper - WUB (Blue is Primary) Grixis - UBR (Black is Primary) Jund - BRG (Red is Primary) Naya - RGW (Green is Primary)
Wedges are the three color groups made up of one color and it's two enemy colors in the WUBRG circle. Abzan - WBG (Black is Primary) Jeskai - URW (Red is Primary) Sultai - BGU (Green is Primary) Mardu - RWB (White is Primary) Temur - GUR (Blue is Primary)
@sorinjace Rakdos(BR) is non-white's primary. uBRg. Because green and blue are next to white if we see them in the WUBRG circle. It's just my opinion though.
It's a difficult design space to say the least, as this was the hardest contest I've ever judged. To me it's about getting color representation on the four colors you DO have as well as trying to keep the missing color out of the mix. I don't know that you have design space to designate a "Primary" color in and amongst all of that, but I like @Tomigon's approach.
Comments
Bant - GWU (White is Primary)
Esper - WUB (Blue is Primary)
Grixis - UBR (Black is Primary)
Jund - BRG (Red is Primary)
Naya - RGW (Green is Primary)
Wedges are the three color groups made up of one color and it's two enemy colors in the WUBRG circle.
Abzan - WBG (Black is Primary)
Jeskai - URW (Red is Primary)
Sultai - BGU (Green is Primary)
Mardu - RWB (White is Primary)
Temur - GUR (Blue is Primary)
Maybe two colors that aren't placed next to the missing color in the WUBRG circle.
Rakdos(BR) is non-white's primary. uBRg. Because green and blue are next to white if we see them in the WUBRG circle.
It's just my opinion though.
From Guildpact - The Nephilim
From Commander 2016
For Commander 2016 WotC gave the combos names and themes
Chaos - UBRG
Aggression - BRGW
Altruism - RGWU
Growth - GWUB
Artifice - WUBR
On MTGCS we had an awesome two-part contest around this thanks to @StrongBelieves
http://forums.mtgcardsmith.com/discussion/2111/phase-alpha-operation-box-contest-one/p1
http://forums.mtgcardsmith.com/discussion/2249/phase-beta-operation-box-contest-two/p1
It's a difficult design space to say the least, as this was the hardest contest I've ever judged. To me it's about getting color representation on the four colors you DO have as well as trying to keep the missing color out of the mix. I don't know that you have design space to designate a "Primary" color in and amongst all of that, but I like @Tomigon's approach.
Yep, Sultai. My bad!