Monsieur Antoine Auguste Le Blanc. (Sophie Germain, 1776–1831)
Sophie Germain hid behind the male pseudonym "M. Le Blanc" to study at the École Polytechnique and to be taken seriously in mail correspondence with other mathematicians, including Lagrange and Gauss.
It seems to me to be much more than merely an analogy, because (assuming DC) the ascending chain condition is exactly equivalent to asserting that the collection of ideals is well-founded under (reverse) inclusion. Thus, one can make arguments by induction on ideals, where each instance reduces to the instances in larger ideals, if any, and it seems that Noether did this quite well. For example, under the ACC, every nonempty set of ideals must contain a maximal element, and this is simply another way of stating the induction principle: to prove $\phi(I)$ for every ideal, simply prove that if $\phi(J)$ for all $J\supsetneq I$, then $\phi(I)$, since this will rule out a maximal element of the set $\{I\mid \neg\phi(I)\}$, which must therefore be empty. When the ACC holds, therefore, one may assign an ordinal rank to every ideal, in the manner that any well-founded relation supports such ranks, namely, the maximal ideals get rank 0, and penultimate ideals get rank 1 and so on, with the rank of an ideal equal to the supremum of the ranks+1 of the ideals properly containing it.
So my perspective is that the ACC is a quite robust and important instance of well-foundedness, rather than merely analogous to it.
Concerning the history of the terminology, I noticed that the Wikipedia entry on Noetherian induction redirects to the page on well-founded relations, and Wikipedia cites "Bourbaki, N. (1972) Elements of mathematics. Commutative algebra, Addison-Wesley" specifically in connection with this terminology. So perhaps Bourbaki is the origin of the terminology? (See ACL comments below.) Transfinite recursion itself certainly pre-dates Noether, tracing back to Cantor's use of it in the Cantor-Bendixson theorem, which is also the theorem that led Cantor to the ordinals. Meanwhile, the Wikipedia entry on the axiom of foundation asserts that "the concept of well-foundedness and rank of a set were both introduced by Dmitry Mirimanoff (1917)."
Lastly, let me add that one doesn't generally much see this Noetherian terminology used for well-foundedness or well-founded induction in the parts of logic or set theory with which I am familiar, where the use of well-foundedness is pervasive and often a central concern. But I suppose it wouldn't be surprising to find this terminology more commonly used in algebra, because of Noether's successful use of it there.
Best Answer
I have a copy of her biography, Emmy Noether, 1882-1935 by Auguste Dick (translated to English by H.I. Blocher). Appendix A contains a list of 43 publications, apparently complete, and not one is indicated as being published pseudonymously. Of course a few had male co-authors, but that is not the same at all.
Also, I skimmed the text of the book and could find no reference to such a thing.
If Natalie Angier, the author of the New York Times article, is aware of a pseudonymous Noether paper, she would seem to be the only one.
I agree with Allen Knutson that a letter to the paper's corrections department is in order.