Zindagi Tere Naam is a narration by an old man named Mr. Singh (Mithun Chakraborty) to an aged lady who is suffering from Alzheimers. The story he narrates is about two young people Siddharth and Anjali who are in love. Anjali, is born in a wealthy family and her disapproving father takes her away, as Siddharth is poor.
Dejected and hurt, Siddharth resorts to writing letters to her and writes one letter a day, for a whole year. But, none of the 365 letters reach her. Years pass and having not heard from Siddarth, Anjali accepts to get married to another man.
Destined for their lives to cross, the lovers meet again.
As the flashback ends, the story comes back to the old couple. The aged woman shows signs of getting her memory back as she recognizes that Mr. Singh was narrating their own love story, making him a very happy man. It only takes a few moments of joy until she looses her memory again, not recognizing Mr. Singh anymore.