Yes Kevin, I thought maybe I explained it badly so good of you to attempt an answer.
I understand the points/processes you mentioned however … say I have a text layer … in the comp panel it reads “Big Sale” and in the timeline panel in the column headed “Layer Name” the Layer’s Name reflects the Text Layers content in the Comp window eg it says Big Sale … so – rather than create a brand new layer for some more text I just duplicate the layer – in the comp window the dupe says Big Sale of course and also the dupe layer has Big Sale 2 – I then double click the dupe layer this highlights the text in the comp window and I type “Starts Today” and the text in the comp window reads “Starts Today” but sometimes (and only sometimes, that’s my problem, it’s not consistent, the dupe layers name remains “Big Sale” ie it doesn’t always automatically update the layer name to reflect the content of the layer in the comp window !