Lines are always based on individuals, not "human names."
Whether you linebreed on a particular dog from Burns ... or from a particular dog (or dogs) that you have, pure or mixed," to establish a line means (literally) to LINEbreed on some dog (or dogs).
For instance, I linebred on Poncho.
David Tant linebred on Yellow.
Boyles linebred on Dirty Mary.
Some key dog needs to stand out in your mind, as truly superior, and then you will want to start breeding this dog ... and then forming breeding patterns around that dog ... either by breeding that dog back to his daughters, his mother, or breeding his sons/daughters together, etc.
However, you want to be selective as to the traits these dogs have ... you want to maintain the traits of that key dog (not just his name) ... and I know you know what I mean
Here is an indepth article I wrote on The Art of Breeding Dogs ... it's long, but it's worth the read.
Jack