The name Seth in the Bible
After the death of Abel and the expulsion of Cain, Seth remains to become the ancestor of Noah. However, it's by no means certain that all the other families were destroyed in the flood. Noah had a wife and so did his sons. Nowhere in the Bible it is mentioned where they came from, and they might have been Cainites for all we know. The patriarchies of Jabal and Jubal mysteriously managed to survive the flood, and it may very well have been through the wives of Noah and sons.
Since Seth is a ancestor of Christ, his name also appears in the Greek New testament, where it is spelled as Σηθ (Luke 3:38).
Etymology of the name Seth
The meaning or even purpose of the name Seth is a bit of a mystery. One thing is sure: it comes from this extensive verbal cluster:
When Eve names Seth she says, "God has appointed (שית) me another offspring..." (Genesis 4:25), and traditionally readers have understood that therefore the name Seth must come from שית. But this is by no means certain. It may be that the name Seth is really the word שת (shat), meaning national foundation, but the Masoretic punctuation made the name Seth identical to the word for buttocks, and even the assumed contraction of שאון, meaning tumult.
NOBSE Study Bible Name List and Jones' Dictionary of Old Testament Proper Names agree: The name Seth means Appointed. But it has a strong connotation of Foundation (Butt) and Tumult.