[Legate of Amon Lanc]

Originally Posted by Thinlómien

Celeborn was not the official "head of state" any more than Galadriel was. I'm wondering why do we have different views about the matter and which one is correct.

Well, one thing is, because it was Celeborn, not Galadriel, who represented Lórien in the "outside disputations", as much as the head of the state. We read for example in the Appendixes to LotR, that after the War of the Ring, Celeborn goes out and destroys Dol Guldur and then - the main part - he makes "diplomatic talks" with Thranduil and they divide the Greenwood.
But to be correct, the "head of state" was actually neither of them. In Unfinished Tales, "The history of Galadriel and Celeborn" we are told, that

There they dwelt while the Third Age lasted, but they took no title of King or Queen; for they said that they were only guardians of this small but fair realm, the last eastward outpost of the Elves.

But nevertheless, Haldir (and others) take them as their rulers, for our purposes we might think that "Lord and Lady" mean the same as "King and Queen".
In the LotR, all the way from the borders of Lórien to Caras Galadhon, C&G are referred to only together:

'Now you have come thus far, you must be brought before the Lord and the Lady. They shall judge you, to hold you or to give you leave, as they will.'...

'...though the Lord and Lady may know, I do not.'...

...'they bring me a message from the Lord and Lady of the Galadhrim.'...

...'Here is the city of the Galadhrim where dwell the Lord Celeborn and Galadriel the Lady of Lórien.'...

(emphasise mine)
But from then on, when the Fellowship comes before the Lord and the Lady, it is Celeborn who speaks, not Galadriel. Galadriel is the "second voice": I am not saying that she is less important than Celeborn, but that she is something like Melian was: Thingol was speaking and Melian interfered only when she had something to add. Thingol was the one who was first speaking with the outsiders, Beren, the dwarves, whatever. So is Celeborn. Galadriel interferes only when she has something to add. Of course, in the matters she feels important, she acts on her own account - but somehow I get the feeling that the peek into the Mirror is not an "official" thing. And also, when giving the gifts to the Fellowship, Galadriel says "these are the gifts which the Lord and Lady of Lórien offer to you". And few times before, she speaks about - or even to - Celeborn like this:

For the Lord of the Galadhrim is accounted the wisest of the Elves of Middle-Earth,
and a giver of gifts beyond the power of kings.

Says Galadriel. I don't know, somehow I get the feeling that she's treating him with respect... you know, like if they were equal, but Galadriel behaves the way that she treats him as an authority over herself. Yeah, now I think I happened to sum very well what I wanted to explain. The female counterparts of the rulers have the same power, but they willingly treat their husbands as greater authority. Yeah, that's what I had in mind, I hope you understand now what I meant, Lommy.

Originally Posted by Lalaith

The Galadhrim...were they named after Galadriel or is another etymological origin?

Nope, there is something very long written about it in the History of Galadriel and Celeborn in the Unfinished Tales, Appendix E, "The names of Celeborn and Galadriel". The main thing is, that Galadriel's name comes from the word "galad" like in "Gil-Galad" (Starlight, "galad" meaning "light" here) whilst the name of the Silvan Elves Galadhrim comes from the word "galadh" - a "tree", and they called themselves Galadhrim long before C&G even first came there. To extend this, just one quote.

On occasional confusion of Galadriel's name with the word galadh my father wrote:

When Celeborn and Galadriel became the rulers of the Elves of the Lórien (who were mainly in origin Silvan Elves and called themselves the Galadhrim) the name of Galadriel became associated with trees, an association that was aided by the name of her husband, which also appeared to contain a tree-word; so that outside Lórien among those whose memories of the ancient days and Galadriel's history had grown dim her name was often altered to Galadhriel. Not in Lórien itself.