Quick answer
The verse hands a man a title. It is one of the few places the book stops describing a type and names him.
Read both lines
Three words for pride stack up before the name arrives, which is the craft: the reader is buried in the adjectives the way an acquaintance is buried in the behavior, and only then does the label land. "Scoffer is his name" is a formal move, the sort of thing said when a reputation has hardened past correction, and this book has already established that the scoffer is the one figure who does not learn from being corrected. The second line then closes the loop by returning to the behavior. He is called this because of what he does, and he keeps doing it, which is why the name sticks.
Related: Proverbs 21:11 · Proverbs 9:7–8 · Proverbs 22:10 · Proverbs 16:18
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.