I tried, I really did, to go along with the scholarly preference for referring to the work that runs from Joshua through 2 Kings, the Former Prophets as it is designated in the Jewish canon, as the “Deuteronomistic History“. But I’ve decided to go with “Deuteronomic History” not only because “Deuteronomistic History” is cumbersome (and hard for most undergraduates to pronounce), nor primarily because “deuteronomic” seems to be a more appropriate adjective, but because linguistically “deuteronomistic” seems to invite odd understandings of what it might mean.
On the one hand, if one considers the parallel terminology of “art”, “artist” and “artistic”, then presumably a “deuteronomist” would be one creates “Deuteronomy” (or “works of deuteronomy”), and these results would themselves be “deuteronomistic”.
On the other hand, if one considers parallels such as “autism” and “autistic”, one might easily conclude that “deuteronomistic” means “suffering from deuteronomism”. Or, for a more positive parallel, we could look at “optimism”, and then might say that the author of the Former Prophets was “incurably deuteronomistic” in outlook.
So I’m going with “Deuteronomic History” for now, although there are obviously other verbs and adjectives we could create that might be appropriate. For instance, if the author of Joshua-2 Kings used extensive earlier sources and was much more of a compiler-editor than author, then we might talk of the “deuteronomization” of those sources. The result would presumably be deemed “deuteronomatopœia” – something that sounds like, or more precisely, something that makes the same sound as, Deuteronomy.
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