  We unravel the stationary properties and the interaction quench dynamics of
two bosons, confined in a two-dimensional anisotropic harmonic trap. A
transcendental equation is derived giving access to the energy spectrum and
revealing the dependence of the energy gaps on the anisotropy parameter. The
relation between the two and the one dimensional scattering lengths as well as
the Tan contacts is established. The contact, capturing the two-body short
range correlations, shows an increasing tendency for a larger anisotropy.
Subsequently, the interaction quench dynamics from attractive to repulsive
values and vice versa is investigated for various anisotropies. A closed
analytical form of the expansion coefficients of the two-body wavefunction,
during the time evolution is constructed. The response of the system is studied
by means of the time-averaged fidelity, the spectra of the spatial extent of
the cloud in each direction and the one-body density. It is found that as the
anisotropy increases, the system becomes less perturbed independently of the
interactions while for fixed anisotropy quenches towards the non-interacting
regime perturb the system in the most efficient manner. Furthermore, we
identify that in the tightly confined direction more frequencies are involved
in the dynamics stemming from higher-lying excited states.
