According to this website...
http://www.delna.lv/english/ar2000.htm
...in Latvian, "Delna means the open palm of the hand, and most frequently the word is used in the expression 'kâ uz Delnas,' which means roughly 'as plain as the nose on your face' or 'plain as day.'"
However, I kinda doubt that the parents of your Hatian grandmother may have spoken Latvian. In which case I would say that your name of "Delna" is probably an alteration of the name "Delma", from the French "de la mer", meaning "of the sea".
-- Nanaea