What was the name of elderly headmaster at author JK

You are likely thinking of Albus Dumbledore, the headmaster of Hogwarts School of Witchcraft and Wizardry in J.K. Rowling's Harry Potter series.

While Dumbledore is not technically "elderly" at the start of the series, he is considered to be old and wise by the wizarding world. He is the headmaster throughout the series, and he plays a vital role in the story.