DAGG-mar as in "daggmask" (earthworm). I'm Swedish and I think the Danish has a softer pronounciationa (mushy we say about the Danish pronounciation in Sweden, unkind neighbours as we are ;)
Dagmar sounds very old-fashioned to me, I prefer
Damaris which to me sounds exotic.
"You sought a flower and found a fruit. You sought a spring and found a sea. You sought a woman and found a soul. You are disappointed." (
Edith Södergran 1891-1923)