JY---
What do you think of this explanation of Céadach?
'* Brigh: This Irish word seems to he the root of the surname Bright. The name Ceadach ("cead:" Irish, first; Chald. "chad") implies "the foremost man;" and Ceadach na Brighe means "the man who was foremost for his strength."'
http://www.libraryireland.com/Pedigrees1/TraceyHeber.php