According to J.R.R. Toljien canon (maps, footnotes, or even the books themselves) what was the name of the lake from which the Watcher in the Water guarded the entrance to Moria?
It didn't have a name; nobody expected it to be there:
'Ah! Here it is at last! ' said Gandalf. `This is where the stream ran: Sirannon, the Gate-stream, they used to call it. But what has happened to the water, I cannot guess; it used to be swift and noisy. Come! We must hurry on. We are late.'
They found the stone steps without difficulty, and Gimli sprang swiftly up them, followed by Gandalf and Frodo. When they reached the top they saw that they could go no further that way, and the reason for the drying up of the Gate-stream was revealed. Behind them the sinking Sun filled the cool western sky with glimmering gold. Before them stretched a dark still lake. Neither sky nor sunset was reflected on its sullen surface. The Sirannon had been dammed and had filled all the valley.
Fellowship of the Ring Book II Chapter 4: "A Journey in the Dark"
Since Gandalf and Aragorn spent quite a long time looking at maps in Rivendell, if the Elves had a name for this pool presumably one of them would have known about it; if any other peoples has a name for it (other than "the pool"), we're not told about it.
After hunting through History of Middle-earth, I feel confident in saying that it had no (known) official name.
The Book of Mazarbul calls it "the pool", which seems to be the nearest thing to a name that it ever gets:
The pool is up to the wall at West-gate.
— The Lord of the Rings II 5, "The Bridge of Khazad-dûm"
Speculation time: While it was certainly new for it to fill the valley, it's not necessarily the case that there was not previously a lake or pool in valley before the West-gate. There may have been a much smaller one. So while we don't know any real name for it, we can't assume that it didn't have one because it was new and unexpected.