Suppose I want to maximize $u=c_1+c_2$ subject to a budget constraint $p_1c_1+p_2c_2\leq m$ and a requirement $c_2<\overline{c_2}$ that must be satisfied. The source of the $c_2<\overline{c_2}$ requirement is not important but you can think of it as a physical or legal limitation that makes it impossible to consume $\overline{c_2}$ or more.
I can write this problem as
$\max\limits_{c_1,c_2} \Big\{(c_1+c_2) -\lambda(p_1c_1+p_2c_2-m)-\rho (c_2-\overline{c_2})\Big\}$ where $\rho=\begin{cases}\infty & \text{if $c_2 \geq\overline{c_2}$}\\0 & \text{otherwise}\end{cases}$.
My question is what do you call $\rho$? It isn't a Lagrange multiplier like $\lambda$ because the value of $\rho$ is fixed exogenously by the modeler. But it functions similarly in that it penalizes violation of the constraint. Would you call it a loss function? A penalty?