Haleth's dates are barely even hinted at in The Silmarillion (apart from the fact that she clearly lived soon after the coming of Men into Beleriand). The dates given here are taken from a genealogical chart given in volume XI of The History of Middle-earth, and thus cannot be considered canonical, although they do place Haleth in the right period of Middle-earth's history.

From a certain point of view, Haleth founded this house, or at least gave it her name. However, Haleth herself was childless and left no direct descendants, being succeeded by her nephew Haldan. For that reason, the house that followed her should perhaps more properly be known as the House of Haldad (after her father, who was the common ancestor of all the rulers of the Haladin). Nonetheless, Haleth was such an important figure in the history of her people that her name became attached to the House of her successors.

This interpretation is open to question. The name 'Haleth' was also used for a son of Helm, and there it is clearly from Old English hæleþ, meaning 'warrior', 'hero' or just 'man'. It's unclear whether the name of Haleth of Brethil derived from the same root, but no other intepretation is available. Note that when Haleth was first created by Tolkien, he envisaged this character as a man ('Haleth the Hunter') so this masculine name would not necessarily have been out of place.