For example, Esper refers to decks made up of White, Blue and Black cards.
What are the names of the other colour combinations? In particular, how do we refer to a Red-White-Black deck?
Most decks with a single color are not competitive in tournaments (due to the fact you're settling for the top ten cohesive cards in a color instead of two sets of the top five in two colors. The difference in power level between the top 1-5 and the top 6-10 can be massive and game deciding. The other colors also make up for each others weaknesses.) But they do exist, and are referred to as "Mono X".
Each of these corresponds to a guild of Ravnica. Since the guilds were released (and especially now that we've returned) the color pairs have become common names for duo-color decks. Both allied and enemy color pairs are common to see, although allied more so (due to higher deck cohesion).
The first of these are the shards of Alara. They jive well because they give two sets of allied colors each. The less commonly used are the wedges, which involve two enemy color combinations: they're derived from the dragons of Planar Chaos, the volver cycle from Apocalypse, or more recently the five clans from Khans of Tarkir. Having only one allied color pair (the two enemies of a single color will be allied) limits deck cohesion, making their use infrequent.
More typically, enemy three color decks are not fully fleshed out in the colors. You're more likely to have an "Izzet splashed with green" deck than a "Ceta" deck.
In addition, it's especially common for red + blue + green and black + blue + green to be called by their abbreviations — "RUG" and "BUG" — because these are names that are easy to remember and pronounce.
Most decks do not have four full colors. As with three color enemies, if they reach this many colors, it's a shard with a splash of another color. So you're more likely to see something like "American splash black" instead of "Yore".
Names for four-color identities come from one of two sources:
So the four colour identities' names are:
Decks with all five colors usually revolve around a single combo that they hope to pull off. It takes a lot of mana fixing and a massive amount of playtesting to get a reliable five color deck. For this reason, you don't often find them in tournaments. You find them often in Commander (giving the player access to every card ever, greatly increasing the power level of the deck) and in skill challenges where a player just tries to come up with a crazy deck idea to see if he can make it work. Obviously there's only one five color deck, it uses all five:
Sometimes, four color decks will also be called Rainbow just because they have so many colors.
Sometimes, particularly in formats with a very large card pool, you'll see colorless decks as well. The most common name for these is a reference to the old card frame for artifact cards:
Mono brown (not to be confused with BrownTown which is a draft deck leaning heavily on minotaurs)
Some newer colorless decks have come to be referred to as "Diamond" decks in reference to the diamond-like new symbol for colorless mana
As noted by others, the 'aligned' color triplets - that is, those that consist of a color and its two siblings to either side on the usual Black-blUe-White-Green-Red color wheel - have nicknames (but not formal names!) based on their 'shards' in the Shards of Alara block: Esper (Ubw), Bant (Wug), Naya (Gwr), Jund (Rgb), and Grixis (Bru).
As for the non-aligned color triplets (which of necessity are one color and its two enemies), the 'dragon' scheme that Lee Abraham mentions based on the names of the dragons that were in Planar Chaos (Intet for Urg, Oros for Wrb, Vorosh for Gub, Numot for Rwu and Teneb for Bgw) is one that I've seen; the other (and slightly more common, at least in the playgroups I play with) is based on the 'shards' that were in Apocalypse, the original 'enemy colors' set - there's a consistent name there that's used on both enchantments and creatures that care about the enemy-color combinations. That set is:
I've seen some people call the other color combos by the names of the elder dragons.
For instance RWB - Oros after the card Oros, The Avenger. Other times I've seen them called based on a national flag that contains their colors. For instance RWU is regularly called American.
However the moment there are no "official" names for the wedge colored decks.
Other answers have addressed the 3 color combinations (aka Allied colors correspond to the Shards of Alara and Enemy colors are much less clear) but the two color combinations correspond to the guilds of Ravnica:
WU - Azorius
WB - Orzhov
WR - Boros
WG - Selesnya
UB - Dimir
UR - Izzet
UG - Simic
BR - Rakdos
BG - Golgari
RG - Gruul
Bant - primary white, secondary blue/green
Esper - primary blue, secondary white/black
Grixis - primary black, secondary blue/red
Jund - primary red, secondary black/green
Naya - primary green, secondary red/white
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