I was trying to find names with a Y to balance the Y in Cygnet. I found some interesting names in this search
Boyana, Chessa, Sessy (really like the last two). anyway, do any of these work for you?
Twilight Cygnet
Cybill Cygnet
Cecily Cygnet nn Sessy
Chessa Cygnet nn Chessy
Cosma Cygnet
Florence Cygnet nn Flossy
Ramona Cygnet
Xylon Cygnet
Xylina Cygnet
Cyprienne Cygnet
Darby Cygnet
Boyana Cygnet
Bowin Cygnet
Gilby Cygnet