I am aware that black holes can move through space-time. Is there a way to move a naked gravitational singularity artificially? Sorry if this is a little stupid, trying to figure out the feasibility of singularity propulsion.
I prefer to not talk about gravitational singularities because I expect quantum gravity theory to prevent them.
In principle, you can move a black hole by gravitational attraction. Just drag a massive object past it, eg a neutron star. One way to do that is to set off a supernova of the appropriate size in the vicinity in such a way that the supernova remnant goes where you want it to. Figuring out how to do that safely & predictably is left as an exercise for the reader. ;)
And if it's an electrically charged black hole you can use electrostatic attraction; if it's uncharged, just throw a bunch of charged particles at it first to charge it up. But you'll need to work fairly quickly because charged black holes probably don't hold their charge for long.