Cyclic orderings are somewhat rare beasts but they do show up here and there. A set with a cyclic ordering is a "cyclically ordered set", just as a set with a total (or partial) ordering is a "totally (or partially) ordered set". The formal definition of a cyclic ordering is found in http://en.wikipedia.org/wiki/Cyclic_order. Its just a certain kind of ternary relation on a set.
I suppose if you wanted to mimic "poset" for "partially ordered set" you could say "coset", but I would not advise it :-) and for an exhaustive list of the most common alternatives see the link above.