It is a Croton, yes,and it can be pruned back to encourage new,bushy growth, but it should be done in stages. With long,lanky and bare stems such as you have, its recommended to reduce them by a third; allow the plant to recover by producing new leaves and growing on a bit, then reduce again, as suggested in this link https://homeguides.sfgate.com/trim-croton-71540.html. The other option is to reduce a third of the existing stems down to the lowest leaf or leaf joint, and leave the others alone, carrying out he same procedure next year on the ones you do not prune now. If you can increase its light levels, that will help it produce new bushy growth, and use houseplant food immediately after cutting back and as often as recommended on the pack during the growing season - reduce or stop fertilizer in Fall
If you're worried about how low you can prune (because it wasn't done for a long time), cut to the lowest leaf as Bamboo said, but don't discard the pruned branches. Try to root them as well. Fall is not the right time. You may postpone it to spring or use propagators with bottom heating. There are chances that cutting too low (down to a very old stem portion) will leave you with a "blind" stem (having no buds). That is where the rooted cuttings may prove helpful. If your cuttings have rooted, then you can take the risk.