Yes, there really is a King David.
In the history of Israel recorded in the bible the most important king is King David. He founded the House of David from which Jesus is descended. All the kings of Judah, the southern kingdom after the split of Israel, were descended from David as well.
In Isaiah 9:7 we see the house of David mentioned “…upon the throne of David, and upon his kingdom…”. Joseph, Jesus’ earthly father, in Matthew 1:20, is referred to as a son of David. Jesus Himself, in Matthew 20:20 is also referred to as a son of David. David is important!
Seeing this, many critics have stated that there is no evidence outside the bible that David was real. They think he was a made-up king the Jews used to support their history, which they also made up. This is just plain wrong!
There is evidence that David and the House of David are real and the history we read in the bible is correct. In 1993 some archaeologists found a stone, referred to as a stela, that contained the phrase “House of David”. This dates from the mid eighth century BC-over 700 years before Jesus was born! That is a long time ago.
This all goes to support the accuracy of the bible as a historical document. So, whenever you hear someone claiming to be an expert on all things ancient, saying things like “there is no evidence that the bible is accurate”, relax. There is a lot of evidence!
You can read more about this on this web page: https://www.biblicalarchaeology.org/daily/biblical-artifacts/the-tel-dan-inscription-the-first-historical-evidence-of-the-king-david-bible-story/