With 3*3*3 you have 3^3 = 27 possibilities. And with maximum 15 companies, that is not much of a problem. As even when you pick the 15:th name you have a possibility of (27-14)/27 = 0.48 of picking a valid name. This is a very high possibility considering the computer power we have available.
But if you only have 16 possibilities the probability when picking the name for the 15th company becomes (16-14)/16 = 0.125, which is still high enough that it will not be a practical problem in our case.
But there are cases when the probability of getting it becomes so low that given the time constraints you have it becomes a problem to choose by random until you find something that works. If you want to dig into this you can read on the RSA-algorithm.
