A pair is a set of two things of the same type that are used together. What do you call a set of three such things? What about four, five, etc.?
It's safe to call 'a set of three' or whatever number you want. Why? Because if the context is not clear, it may sound odd.
Here is the list of, for example, set of 'three' in various cases. Note that for each condition, the word is different. While for three kids delivered it's triplet, for a card game, it would be 'trio.' Furthermore, in cricket, it'd be 'hatrick' when three batsmen are out; 'trilogy' for a tri-series movie.
So, again, to be on a safer side, call 'set of ' when the context is not clear. Say, you buy a set of three shelves from some store.