Eämbar (Q. 'Sea-Home'), a floating Numenorean headquarters.
Alcarondas (Q., meaning unclear)/Aglarrâma (Ad.), the 'Castle of the Sea', Ar-Pharazon's great ship. Its name contains 'alcar', glory (and in Adunaic, 'aglar').
Every one of these ships is named in Quenya - right down to the one built by the biggest elf-hater of them all. Clearly, that's just how ships are named; since Tuor and Eärendil both learnt the art from Cirdan, they probably picked the habit up from him, as well.
Further, we can point out that every name has meaning. You don't name your ship after your mother or what have you - you name it after its role (as Entulessë), or as a description (Alcarondas, probably), or in one case after your house (Eärrámë - Tuor was the Lord of the House of the Wing in Gondolin). So that's answer number one.
But... every one of those ships was built by men - six of them, in fact, by Numenoreans, and the other two by the father and grandfather of Elros Tar-Minyatur, first King of Numenor. We know that the elves built ships, too - at Alqualonde, on the Falas, on Balar, at Mithlond and Edhellond. But of all those ships - the Swan-Ships of the Teleri, the ship of Amroth - we are never given a personal name. The only Elf-built ship which does have a name is the ship that bears the Ringbearers West - and it's known simply as 'The White Ship'. Tolkien could certainly have slipped in the Quenya form, Lossecirya or Ciryalosse, but he chose not to.
So do the Eldar actually name their ships? Given how the Teleri thought of theirs - as practically alive - I'm tempted to wonder whether they believed that each ship had its own name, intrinsic to it - and not discoverable by them (at least, not yet). On the other hand, these are elves we're talking about; their whole thing, right from the start, was assigning names to things, and awakening them.
I don't know. But I'm reminded of Philosopher at Large's comment on the fact that the Silmarillion doesn't bother to name the Ten who stood by Finrod when he left Nargothrond - because it is the elven history of Middle-earth, and they already know who they are. Could it be that the individually-crafted ships of Cirdan and the Teleri are so unique that they don't need names - that the Eldar can tell which ship they're seeing at a glance, and know which one you're talking about just by the character you describe.
It would be incredibly tricky to write - but at the same time fascinating.