I think it is indeed van der Waerden, but in the earlier paper [1926], where he sounds just like one does when introducing terminology: translated from p. 143,
the proposition in question is an almost immediate consequence of two fundamental propositions of HILBERT, which can be described as HILBERT’s Nullstellensatz and HILBERT’s Basissatz.
An extra twist is that this all ‘presumably’ first appeared in Dutch, in a first version [1925] of the paper that would be interesting to find and check; it doesn’t seem to be online.
[1926] van der Waerden, B. L., Ein algebraisches Kriterium für die Lösbarkeit eines Systems homogener Gleichungen., Proceedings Amsterdam 29, 142-149 (1926). ZBL52.0125.01.
[1925] Van der Waerden, B. L., Een algebraies kriterium voor de oplosbaarheid van een stelsel homogene vergelijkingen., Verslag Amsterdam 34, 1123-1130 (1925). ZBL51.0092.05.