Why the Iroquois people referred to themselves as the Haudenosaunee?

That is a common modern myth generated by misleading internet sites and badly informed or completely ignorant writers. The tribes making up the Iroquois League each spoke their own different language - these are closely related, but different. So it would clearly be wrong to think that they all called themselves by the same single name.

The Word Hodenosaunee is just one version of the term for "people of the longhouse", which is Hotinonsonni, Haudenosaunee, Hodenosaunee, Ongwanosionni in the languages spoken by the tribes of the League. In Cayuga the term Hodinǫhsǫnidǫh (longhouse people) refers to their own tribal leadership, not to the League.

The Oneida Word for a longhouse is kanúhses, by the way. In Cayuga it is ganǫhses.

In each of their languages, each tribe had their own Words for the other Iroquois tribes, so the Oneida called the Senecas tsitwanaˀa·ká (people of the mountains); they called the Onondagas onutaˀkeha·ká· (people of the hills) and they called the Cayugas kayukaˀa·ká (people of the mucky land).

Furthermore, each Iroquois tribe had its own specific name for itself and these self-designations would be used far more frequently than "people of the longhouse". Individual tribal identity was valued very highly, even among allies.