What's the name of the symmetry $ L \to L + \frac{d \Lambda}{dt}$? In the Lagrangian formulation of Classical Mechanics, we have the freedom to add a total time derivative of an arbitrary function $\Lambda$ to the Lagrangian:
$$ L \to L + \frac{d \Lambda}{dt} . $$ 
Does this symmetry of the Lagrangian have any particular name?
 A: Some authors call that a gauge transformation of the Lagrangian function. Others, don't give any specific name and may object to the previous one. 
For a reference for the former denomination, see for instance F. Scheck, Mechanics, Springer, 2010.
A: *

*I would simply call the operation$^1$
$$L(q,\dot{q},\ldots, q^{(N)},t)\quad \longrightarrow \quad L(q,\dot{q},\ldots, q^{(N)},t) \quad+\quad \frac{dF(q,\dot{q},\ldots, q^{(N-1)},t)}{dt}\tag{1}$$
for "adding a total derivative term to the Lagrangian",
nothing else.

*A quasi-symmetry transformation or a gauge transformation are by definition specified at the level of the fundamental variables of the theory (in this case, the $q$s and $t$). The operation (1) doesn't in general fulfill this.
--
$^1$ The operation (1) should be amended with a prescription for the possible new boundary conditions (BCs). Note that the operation (1) [with the new BCs] may render the functional/variational derivative of the action $S$ ill-defined. However, if the functional derivative $\frac{\delta S}{\delta q}$ exists both before and after the operation (1), it is unchanged, cf. e.g. this Phys.SE post.
