I don't know of one that seems sufficiently general. The theory's at an intersection:

1. It (in its untyped guise) one of the four most important Turing-complete computation systems;
2. It is algebraically natural, connected fundamentally to Cartesian-closed categories (though with horrid baggage around alpa-equivalence);
3. It is a foundational theory, possibly the theory that best captures the notion of schematic function; and
4. It plays an important role in philosophical logic, due to its link to natural deduction, which is among the few treatments of formal logic that is relevant to how we reason.

Maybe a name formed out of keywords from several of these domains would give a suitable term? How about Cartesian computation calculus?

I don't know of one that seems sufficiently general. The theory's at an intersection:

1. It (in its untyped guise) is one of the four most important Turing-complete computation systems;
2. It is algebraically natural, connected fundamentally to Cartesian-closed categories (though with horrid baggage around $\alpha$-equivalence);
3. It is a foundational theory, possibly the theory that best captures the notion of schematic function; and
4. It plays an important role in philosophical logic, due to its link to natural deduction, which is among the few treatments of formal logic that is relevant to the actuality of how we reason.

Maybe a name formed out of keywords from several of these domains would give a suitable term? How about Cartesian function-calculus?

Edited