"Old Man" was Benjamin Sisko's nickname for the Curzon host of the Dax symbiont, which he continued to use with later hosts of the symbiont. He used it both with Jadzia and Ezri Dax. (DS9: "Emissary", "Afterimage")

Sisko also called Yedrin Dax "Old Man" when they met on Gaia. (DS9: "Children of Time")

When Jadzia decided to stay on Meridian in 2371, which would have meant the two would not see each other for sixty years, Jadzia joked that she could call Sisko "Old Man" when they would see each other again. (DS9: "Meridian")

Benjamin Sisko also occasionally named himself "Old Man" when talking to his son Jake. Benjamin's father Joseph Sisko did likewise when speaking to Benjamin. (DS9: "The Nagus", "Homefront")