“Similarly, Derick’s name is a variation of his late dad’s name, Rick, that his parents created by adding ‘de’ to the front of Rick to spell, ‘de’-“rick,’ literally meaning son ‘of’ (de) Rick,'” Jill and Derick explained. “We were excited to settle on the name Frederick and incorporate both Derick’s and his dad’s name, by just adding ‘Fre’ to the beginning of Derick’s name.”

Source: https://www.distractify.com/p/jill-duggar-new-baby-name