Initial value generator in a circuit (Anfangswertgenerator)
I do not know if it has a specific name. See slide 24 of this resource.
Consider an inductor with inductance \$L\$ and an initial condition \$i_L(0) = i_0\$. The differential equation describing its behaviour is
$$v_L(t) = L \frac{d\ i_L(t)}{dt}$$
Applying Laplace transform,
$$V_L(s) = L (s I_L(s) - i_0)$$
A person given only the above equation, if asked to draw the component or circuit corresponding to it will say that above equation corresponds to a circuit which looks like the diagram below (from the mentioned link)

The figure shown in the question is just the source transformed version of the same circuit (it is also shown in the mentioned link).