I saw in Igros Kodesh 11, page 73 mentioned in the Chida in the name of the Yerushalmi that the name Ben Tziyon is a Segula for a long life and good years. What is the reason that this name has such a strength?
The segula that the name "Ben Tzion" is associated with long life is also brought by R' Rachamim Nissim Yitzchok Palagi in Yafeh La-Lev (Chelek Gimmel Y.D. Siman 265 Ois 7). He connects it with two Pesukim in Tehillim:
שיר המעלות הבטחים בה' כהר ציון לא ימוט לעולם ישב - A song of ascents. Those who trust in the Lord are like Mount Zion, which will not falter but will abide forever. (125:1)
כטל חרמון שירד על הררי ציון כי שם צוה ה' את הברכה חיים עד העולם - As the dew of Hermon which runs down on the mountains of Zion, for there the Lord commanded the blessing, life forever. (133:3)