Dagmara:
1) combination of Celtic "good" and Old
German "famous"
2) a form of the Danish name
Dagmar:
a) modern Danish form of the Old Norse name Dagmær "day" + "virgin"
b) Danish form of the Slavic name Dragomira "dear, kind" + "peace, world"
The original Danish pronunciation is DOW-mar ("dow" like in Dow Jones index, "mar" like in March).
Regards,
Satu