The Caesar haircut gets its name from one of the historical world leaders, going by the same name (Caesar), who often appears in many depictions wearing this hairstyle. He is not a recent figure, with historians putting his birth-date at July 13th in the year 100 before Christ. Yet his impact continues to be felt in many areas of life, with many other things being named after him, besides the Caesar haircut; including the calendar month of July (after his first name, Julius), and the maternity procedure known as Caesarian section; to recall but a few of the many things named after this Roman ruler.
To be sure, it is not clear whether Julius Caesar was the first person to wear the haircut named after him. For all we know, it could have been a popular haircut of the times - one that he found and took fancy of. Or it could yet indeed be an invention of his own; for Julius Caesar was a man quite given to invention. What is clear is that he is the person who popularized it, and courtesy to whose wearing of it, the Caesar haircut has survived the millennia, so that it is still widely worn (and still widely considered relevant) up to this date.