We use a sample of z = 0 galaxies visually classified as slow rotators (SRs) in the EAGLE hydrodynamical simulations to explore the effect of galaxy mergers on their formation, characterize their intrinsic galaxy properties, and study the connection between quenching and kinematic transformation. SRs that have had major or minor mergers (mass ratios ≥0.3 and 0.1-0.3, respectively) tend to have a higher triaxiality parameter and ex-situ stellar fractions than those that had exclusively very minor mergers or formed in the absence of mergers ('no-merger' SRs). No-merger SRs are more compact, have lower black hole-to-stellar mass ratios and quenched later than other SRs, leaving imprints on their z = 0 chemical composition. For the vast majority of SRs we find that quenching, driven by active galactic nuclei feedback, precedes kinematic transformation, except for satellite SRs, in which these processes happen in tandem. However, in ≍50 per cent of these satellites, satellite-satellite mergers are responsible for their SR fate, while environment (i.e. tidal field and interactions with the central) can account for the transformation in the rest. By splitting SRs into kinematic sub-classes, we find that flat SRs prefer major mergers; round SRs prefer minor or very minor mergers; prolate SRs prefer gas-poor mergers. Flat and prolate SRs are more common among satellites hosted by massive haloes ($ 10^{13.6}\, \rm M_{\odot }$) and centrals of high masses ($M_{\star } 10^{10.5}\, \rm M_{\odot }$). Although EAGLE galaxies display kinematic properties that broadly agree with observations, there are areas of disagreement, such as inverted stellar age and velocity dispersion profiles. We discuss these and how upcoming simulations can solve them.