I've read that the Epic of Gilgamesh has potentially inspired bits of the Bible as well as Homer, but I'm wondering if the name Gilgamesh, or his story or any of the characters, were well-known? Did his popularity survive long past the most recent tablets known, from 1200 BCE, or was the story and the characters lost to time?
The bulk of the tablets that make up the most complete edition we have actually come from Ashurbanipal's library at Nineveh, which was destroyed in 612 BCE. Rassam's tablets come from Babylon and have been dated to the Neo-Babylonian Empire (6th century BCE) and subsequent Persian period (from 520ish BCE onwards). It's extremely likely that the biblical flood story was inspired by the Standard Babylonian (SB) version of Gilgamesh, though of course only the flood and perhaps the snake (in the garden of Eden) were adapted from it.*
After this, it's difficult to tell. There certainly are later tablets from Uruk containing Gilgamesh stories, and these might be as late as the Seleucid period - that would put them anywhere between 312 BCE and the 1st century BCE. However, it's uncertain whether these parts belong to the SB version or are independent compositions; they are not part of the attested parts of the SB epic, but might fit in some of its (significant) lacunae. Another trace is Berossus, a Babylonian monk of the 3rd century BCE, who wrote an account of Babylonian history in Greek. He narrates a couple of stories, most significantly that of Zi-ud-sura (he calls him Xisuthros), the flood hero on whom Uta-napishti is based in the epic of Gilgamesh. None of his writings survive independently, only in quotations by later Greek and Roman authors, so it's again difficult to say whether he would've known about the epic in its SB form.
In any of these cases, it's clear that the story had a lasting appeal - certainly it survived the Persians, who had conquered Babylon, as the Seleucid Uruk fragments show.
Source for all things SB Gilgamesh: Andrew George, The Babylonian Gilgamesh Epic: introduction, critical edition and cuneiform texts, Oxford: OUP (2003).
*There is one other possible connection between Gilgamesh and the Bible, but it's really tenuous: there's an almost verbatim translation of the saying "a triple-stranded cord is not easily broken" in Qoheleth (Ecclesiastes) - but that's probably a really late composition so who knows how it got there...
Hormuzd Rassam was Chaldean. My parents were born in villages near the place where he discovered the tablets. I'm proud to be Chaldean. I wish I could visit all the places of ancient Assyria/Mesopotamia. It's my culture and it makes me sad that I can never visit the heritage of my family. Seeing these posts about our culture gives me hope and makes me happy. Thanks for having an interest in our history.