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Hmmm, my mom is Nelda, and her name is here. It says it's a short form of names ending in -nelda or a combo of Nell & the "popular name suffix da".
I know it was chosen b/c my grandmother is Nellie....
Maybe Nilda would be a short form of Burnilda, et. al. as you listed. Even if that's the most common form, maybe that's where is started out.