"Living a life worth remembering is a path to immortality". I think that was from Bruce Lee.
Think of people who lived in the past. We know them because they have done something extra-ordinary, something that propels humanity forward! For me, I think of people like Charles Darwin, Einstein and Galileo, Neil Armstrong...
For the rest, their ordinary lives will just mean they are remembered by their children, if they are fortunate enough to have children, and even grand children. Beyond that, most of us will indeed be shortly forgotten.
It isn't a nice thought to be forgotten. But why should people remember us when we have not given them enough to remember us by? If we do go on and affect people's lives, touch their hearts and minds, then perhaps, our memory might be remembered just a little while longer after we are gone.