I listened to the Fink/Marxer recording over and over again while I was proofreading the new Rise Again Songbook. This is what I hear, which is just a bit different from the DT version and the excellent transcription posted above by Susanne.
Who's singing lead on the Fink/Marxer recording? Her voice is wonderful.

NAMES (Cathy Fink) A patchwork of thousands of precious names There must be someone that you know Woven together in a quilted frame Names the loved ones won't let go CHORUS And I know that my name could be there And I feel the pain and the fear And as human love and passions do not make us all the same We are counted not as numbers, but as names We grieve for the lovers and the families And I pray they'll meet again some day But until that time I will carry the flame As the numbers grow we'll not forget their names A lover, a carpenter, a father, a friend A sister, a minister, a mom Each quilted piece holds a memory Each memory helps us to go on

NAMES (DT Version) (Cathy Fink) A patchwork, thousands of precious names Must be someone that you know Woven together in a quilted frame; Names the loved ones won't let go CHORUS: And I know my name could be there And I feel the pain and the fear And as human love and passions do not make us all the same We are counted not as numbers, but as names. We grieve for the lovers and the families And I pray that they'll meet again some day. But until that time I will carry the flame As the numbers grow we'll not forget their names. A lover, a carpenter, a father, a friend, A sister, a minister, a mom Each quilted piece holds a memory Each memory helps us to go on. filename[ NAMES DS

https://www.youtube.com/watch?v=aEGqSZvTCiE