Dagmar is a Scandinavian and German female name meaning “day maid” made up of Old Norse elements dagr (day) < Proto-Germanic *dagaz which derives from an uncertain etymology though it’s been linked to PIE root *dʰegʷʰ- (to burn); and mær (maid, girl; and, in a more poetic sense, daughter).
I’ve also seen Dagmar listed as being an Old Danish form of Slavic Dragomira, the feminine form of Dragomir meaning “dear, precious + peace; world”
Origin: Proto-Indo-European; Proto-Slavic
Meaning: “day maid”; could also have originated from Slavic Dragomira “dear, precious + peace; world”
Frederick is the English form of Friedrich, a Germanic male name meaning “peaceful ruler”, made up of Germanic elements frid (peace) and ric (ruler); frid comes from Proto-Germanic *friþuz (peace, tranquility) via *frijaz (free) which ultimately derives from PIE root *preyH– (to love); and ric via Proto-Germanic *rīks (king, ruler) which ultimately derives from PIE root word *h₃reǵ- (to straighten, to right oneself).
Frederick is also an English surname originating from the given name.