Lee-Roy - Each seedling - regardless of how it looks - is unique. It is NOT an exact duplicate to any other daylily, just a child of the registered parent plant. To get a duplicate you would have to divide and share the registered daylily. It is getting harder to come up with unique names for daylilies. With almost 80,000 registered ... that is probably one of the biggest challenges of a hybridizer!
And I agree, that the possibility is there to have a seedling look very similar to one of the parents. Example is CCC02:
My seedling looks a lot like the pollen parent. If you look back into the pedigree of the pod parent, you will see that the same registered daylily is also on that side of the family line, too. Which is why I believe it turned out to look so much like the pollen parent. Dominating the characteristics for this cross. I had a second seedling, and it too, looked very similar.
And no, a plant that looks similar would NOT necessarily adopt a part of the F1 parent's name that it resembles. In fact, if it looked that much like the registered plant, why would you even name and register it? Unless it has other outstanding traits that the F1 parent does not have, it would seem redundant to me. But that might also explain why there are close to 80,000 registered daylilies in the AHS database. Many probably do have a close resemblance to another one somewhere in the database.