The story
To quote from Optimization in economics and finance : This terminal condition on λ(T) has often been called a transversality condition, for historical reasons deriving from time-optimal problems, where the (variable) time T to reach a target is minimized. In that situation, the transversality condition appears as a description of how the optimal path crosses a terminal line (graphing state against T).
Etymology from Wiktionary, CC BY-SA 4.0.