  In the present study we analyse the effect of the density dependence of the
symmetry energy on the hyperonic content of neutron stars within a relativistic
mean field description of stellar matter. For the $\Lambda$-hyperon, we
consider parametrizations calibrated to $\Lambda$-hypernuclei. For the $\Sigma$
and $\Xi$-hyperons uncertainties that reflect the present lack of experimental
information on $\Sigma$ and $\Xi$-hypernuclei are taken into account. We
perform our study considering nuclear equations of state that predict two solar
mass stars, and satisfy other well settled nuclear matter properties. The
effect of the presence of hyperons on the radius, the direct Urca processes,
and the cooling of accreting neutron stars are discussed. We show that some
star properties are affected in a similar way by the density dependence of the
symmetry energy and the hyperon content of the star. To disentangle these two
effects it is essential to have a good knowledge of the equation of state at
supra-saturation densities. The density dependence of the symmetry energy
affects the order of appearance of the different hyperons, which may have
direct implications on the neutron star cooling as different hyperonic neutrino
processes processes may operate at the center of massive stars. For models
which allow for the direct Urca process to operate, hyperonic and purely
nucleonic ones are shown to have a similar luminosity when hyperons are
included in agreement with modern experimental data. It is shown that for a
density dependent hadronic model constrained by experimental, theoretical and
observational data, the low-luminosity of SAX J$1808.4-3658$ can only be
modelled for a hyperonic NS, suggesting that hyperons could be present in its
core.
