To help those who are just starting out with a small sample of birds, it might also be worth noting the following. I don't say this to continue the "line name" conversation, so much as to add to folk's thinking.
We've been breeding a few lines for years and years. When I send someone a box of eggs and they happily hatch out 7 or 8 chicks, yes, they have some of our line of birds. But, and this is important, I think, they only have a very small slice of that line. We have over 70 Rocks on the ground, between our three farms. All someone gets in a box of eggs is a small sample of the flock's much wider DNA.
Not only does a new breeder make the out-years choices and decisions but that line itself a fork, a small side stream flowing off from a much larger river. These two families may well evolve differently over the next 5-10 years even if no one dares to outcross.
I got 4 little birds from Jim that are from Don Nelson stock, twice removed already. Neither Jim nor I know what the "in between" breeders did either. Four birds. That's all. If the good Lord is good and we're vigilant, we'll turn those 4 birds into 50 next year. I hardly have any idea whether the four birds we have are even a decent representation of what Don bred for. I have no idea. I got what I got. (giddy happy, btw)
But Bob talked often about this and saw this divergence as a possible good thing for when the time comes, those subset gene pools can be re-united for vigor if needed.