  Recent Baryon Acoustic Oscillation (BAO) measurements released by DESI, when
combined with Cosmic Microwave Background (CMB) data from Planck and two
different samples of Type Ia supernovae (Pantheon-Plus and DESY5) reveal a
preference for Dynamical Dark Energy (DDE) characterized by a present-day
quintessence-like equation of state that crossed into the phantom regime in the
past. A core ansatz for this result is assuming a linear
Chevallier-Polarski-Linder (CPL) parameterization $w(a) = w_0 + w_a (1-a)$ to
describe the evolution of the DE equation of state (EoS). In this paper, we
test if and to what extent this assumption impacts the results. To prevent
broadening uncertainties in cosmological parameter inference and facilitate
direct comparison with the baseline CPL case, we focus on 4 alternative
well-known models that, just like CPL, consist of only two free parameters: the
present-day DE EoS ($w_0$) and a parameter quantifying its dynamical evolution
($w_a$). We demonstrate that the preference for DDE remains robust regardless
of the parameterization: $w_0$ consistently remains in the quintessence regime,
while $w_a$ consistently indicates a preference for a dynamical evolution
towards the phantom regime. This tendency is significantly strengthened by
DESY5 SN measurements. By comparing the best-fit $\chi^2$ obtained within each
DDE model, we notice that the linear CPL parameterization is not the
best-fitting case. Among the models considered, the EoS proposed by Barboza and
Alcaniz consistently leads to the most significant improvement.
