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Dzilna is a very traditional Latvian surname which means green woodpecker in Latvian. Probably this refers to European Green Woodpecker. In Latvian read https://lv.wikipedia.org/wiki/Za%C4%BC%C4%81_dzilna. Species description in English: https://en.wikipedia.org/wiki/European_green_woodpecker for more on this species. (You can find a few people named Dzilna on www.findagrave.com )
Most native Latvians did not have surnames until the 1800's. Most picked nature-based names which translated to Oak Tree, Birch Tree, Bear, Lynx, Amber, etc. Latvians originally from other areas who already had last names just transliterated their German, Swedish, Russian, or other origin of name to Latvian.