[Guinevere]

I think Eowyn Skywalker is right.

Though one must think, because everyone else always called it Moria, as it was by the dwarves in the Hobbit, then the dwarves, out of politeness, would've called it Moria.

I suppose that it would depend on the company that the dwarves were in. With some people, they would've used Khazad-dûm, while with others: Moria.

e.g. Gloin when speaking at the Council of Elrond uses the word Moria:

Some spoke of Moria: the mighty works of our fathers that are called in our own tongue Khazad-dûm

Moreover, on Balin's tomb "was written in the tongues of Men and Dwarves: Balin, Son of Fundin, Lord of Moria" as Gandalf said.
When you read the runes, the lower (smaller) runes mean just that, in English (= the common tongue) while the upper part reads "Balin Fundinul Uzbad Khazad-dumu"
So while speaking in the common tongue, the Dwarves used Moria, and it certainly wasn't any intended insult ore practical joke on Celebrimbor's part!

But one wonders, if it was the Dwarven door, how come Celebrinbor didn't use Runes, instead of Tengwar... after all, it was a stone door, and have you ever tried to carve Tengwar into anything? It's not easy. However, the Runes are all straight lines. How come they didn't use Runes on the gate?

I think they were not exactly carved, but kind of painted with "Ithildin" which contained Mithril.