Maiteder is a name created by Erramun Olabide (1869-1942) and it doesn't seem to be used as word in Basque.
Maite is a Basque given name and a word, meaning "lovable" and "darling". So, the meaning of "darling" for Maiteder is in fact an error, because the first element of the name means that, not all the name.
I checked and the Basque word for "nymph" is "ninfa" (as in Spanish), not "maiteder". In the dictionary of Euskaltzaindia (the Academy of the Basque language), "maiteder" doesn't appear.
But it is true that in Gorka Aulestia's Basque-English dictionary, "maiteder" is equated with "nymph" (it is the only reference in this sense in English, Basque or Spanish). I don't know if it is a very dialectal word, only used by Basque comunities in Nevada.
If you are truly interested about that, you can send an e-mail to Euskaltzaindia.