If you have seedlings and you know the parent flowers, are you required to recognize them in the new name?

No requirement, but people often like knowing what the parentage is.

It would have been nice to carry on the parent's names if known with the seedling like Penang Peach and California Sunset could become Penang Sunset or California Peach. Names could get really creative: Penang Peach and Princess Victoria Rosellini: Princess Victoria Peach? Penang Princess? Or simply Princess Peach? Or how about Penang NOID? California NOID? NOID Princess? FUN.