This lady was born as Kathryn Dawn Lang, that is what her parent's named her, it is her correct name at birth (if internet sources are correct) and capitalisation is correct, as Tim says.
As an adult, she prefers to call herself k d lang, which she is fully entitled to do, and Lianne is right in that you can't say that she is spelling it incorrectly.
As Wikitree encourages people to enter profiles with correct details at birth, there should be some way of presenting her as ''Kathryn Dawn Lang, aka/otherwise k d lang'', which there doesn't appear to be.
Margaret