"Old Man" was Benjamin Sisko's nickname for Curzon Dax who was 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")