Just on a side note for those who are curious,
daoine is the plural for
duine in Modern Irish. (And, yeah, I know there's more than one flavour of Gaelic.
This is just the only one I can speak upon with any education.) It means, quite simply, "people".
Oh, and it should indeed be pronounced "DEE-nah" if using Modern Irish. The exact pronunciation of Old Irish is an academic hot potato, so good luck finding a definitive answer there! Just be aware that the word is something that is still a part of the modern Irish language and thus has a very certain pronunciation there.
Sidhe literally refers to the rounded hills that act as gateways of a sort to the Otherworld, where the Children of Anu (the Tuatha de Danaan) were forced to take up residence. (Please forgive the gross over-simplification here!!!) It came to be a synonym for those people as well, and would actually be a much better choice than Tuatha for referring to the fey folk and their kith.
(
Tuatha is just a word to refer to people from a certain region or area, such as in
fear tuathe or "countryman", and is in no way specific to the people called the Tuatha de Danaan. A
tuath is a kind of political division, but also refers to the people in that division or to any group of regionally related folk in general. Its use in Tuatha de Danaan is just to express that they are "of Danu"/"Anu" and is kind of clumsy to pick out as a specific proper name.)
So, literally,
Daoine Sidhe means "hill people". As pointed out though, the hills in question are something special, so there is much more meaning there beyond the literal. Ermor's Wailing Lady, the
bean sidhe or Banshee, gets her name from the same place. (
Bean simply means "woman".)
Cherryh is a very knowledgeable woman, and somebody I respect quite a bit, but she does tend to gloss a bit. It's hard (if not impossible) not to do, given the complexity of the material and the vast differences between it and the more familiar (to most people) Greco-Roman matter. Other names given to the same people, such as the "fey (fair) folk", were given despite the fear held for them, either for direct contrast or as a form of appeasement. That's the sort of thing she is referring to; it isn't present in
Daoine Sidhe, but IS present in some of the other names for the
Sidhe.