I like directed acyclic graphs and/or DAG because it's a succinct description and contract. Trying to change the name of it makes me quiver with uncertainty.

Quiver (a directed graph with multiple edges) is a standard mathematical term:

https://en.wikipedia.org/wiki/Quiver_(mathematics)

https://ncatlab.org/nlab/show/quiver

A quiver is simply just the data of a category, i.e. a "category" without any of the laws, namely identity and composition.

They're not isomorphic to DAGs since Quivers can have multiple edges between the same set of vertices, directed multigraphs, if you will. There is also no requirement of acyclicity (DAGs are acyclic).

For example, in the category of Sets, vertices are sets and edges are functions between sets, so between e.g. N and N there will be infinitely many edges (all functions between natural numbers) with a particular distinguished identity edge that maps f(n) = n due to category laws. So if you turn the category of Sets to a quiver, you'll have infinitely many edges N -> N and one of them will happen to be the identity function `f(n) = n` but you "forgot" its "identity" relationship/law when you reduced the category to a quiver. This is not a graph, since within your data you need to express that there are other edges between N -> N for example `f(n) = 2*n` is another edge (we can call these multigraphs).

But they aren't DAGs. They are multidigraphs.