  We extend the method of Simpson and Visser (SV) of regularising a black hole
spacetime, to cases where the initial metric represents a globally naked
singularity. We choose two particular geometries, the Janis-Newman-Winicour
(JNW) metric representing the solution of an Einstein-scalar field system, and
the Joshi-Malafarina-Narayan (JMN) metric that represents the asymptotic
equilibrium configuration of a collapsing star supported by tangential
pressures as the starting configuration. We illustrate several novel features
for the modified versions of the JNW and JMN spacetimes. In particular, we show
that, depending on the values of the parameters involved the modified JNW
metric may represents either a two way traversable wormhole or it may retain
the original naked singularity. On the other hand, the SV modified JMN geometry
is always a wormhole. Particle motion and observational aspects of these new
geometries are investigated and are shown to posses interesting features. We
also study the quasinormal modes of different branches of the regularised
spacetime and explore their stability properties.
