  Binary neutron star (NSNS) mergers can be sources of gravitational waves
coincident with electromagnetic counterpart emission. To solidify their role as
multimessenger sources, we present fully 3D, general relativistic,
magnetohydrodynamic simulations of spinning NSNSs initially on quasicircular
orbits that merge and undergo delayed collapse to a black hole (BH). The NSNSs
consist of two identical stars modeled as $\Gamma=2$ polytropes with spin
$\chi_{NS}= 0.36$ aligned along the direction of the total orbital angular
momentum $L$. Each star is initially threaded by a dynamical unimportant
interior dipole B-field. The field is extended into the exterior where a nearly
force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment
$\mu$ is either aligned or perpendicular to $L$ and has the same initial
magnitude for each orientation. For comparison, we also impose symmetry across
the orbital plane in one case where $\mu$ in both stars is aligned along $L$.
We find that the lifetime of the transient hypermassive neutron star remnant,
the jet launching time, and the ejecta are very sensitive to the B-field
orientation. By contrast, the physical properties of the BH + disk remnant,
such as the mass and spin of the BH, the accretion rate, and the
electromagnetic luminosity, are roughly independent of the initial B-field
orientation. In addition, we find imposing symmetry across the orbital plane
does not play a significant role in the final outcome of the mergers. Our
results show that an incipient jet emerges only when the seed B-field has a
sufficiently large-scale poloidal component aligned to $L$. The lifetime
[$\Delta t\gtrsim 140(M_{NS}/1.625M_\odot)\rm ms$] and Poynting luminosities
[$L_{EM}\simeq 10^{52}$erg/s] of the jet, when it forms, are consistent with
typical short gamma-ray bursts, as well as with the Blandford--Znajek mechanism
for launching jets.
