She was named after the Bryce Canyon (Utah) because of its vermilion color.
Her middle name "Dallas" is the city in which she was conceived. This tradition has its origin in her mother's family (Cheryl Howard). The original tradition is to use the grandma's name as the child's middle name, but Ron and Cheryl changed it. According to the original tradition, Bryce's name would be "Bryce Ines Howard".