Can I finish cooking a pork roast next day after partially cooking it

I do not recommend partial cooking of any meat. You risk bacteria growth. Completely cook your meat, and then warm it up again wrapped in foil to maintain juiciness.

Yes and no. You can't safely half cook it. You'd be pulling it out of the cooking process at exactly the point where you'd made it more attractive to bacteria.

You can, however, fully cook it and reheat it. This is a tiny bit tricky with a pork loin, since the optimal temperature for a pork loin is actually somewhat below the temperature that's really safe. You'd want to cook it to at least 140F, a bit more than is really optimal. The best way to do that would be sous vide, though you can also do it in a slow oven. Other roasts, like a shoulder roast, with more fat, would be more amenable to cooking to a higher, safer temperature.

Cool it down quickly, and refrigerate. Then the next day you can reheat it. There are a number of ways to do this; see Reheating pork loin roast for a party for one example. A different tack would be to preheat the oven to 400F, put your roast in it, and turn off the oven. That would quickly put a nice crust on the outside, while gradually bringing the (already fully cooked) roast up to temperature.

A meat thermometer is highly recommended for this. There are too many variables to do it by time, and you want to avoid both under- and over-cooking.

This is an instance where sous vide really works well.

You can pre-cook your pork roast to 140 for 4 to 6 hours in the sous vide the day before. Chill in an ice bath (still in the bag that you cook it in) to bring it down to safe temperature quickly, and then into the fridge.

the next day you can sear it in a number of different ways (broiler, on the grill, in cast iron, either whole or cut into chops and sear individually), and that should be plenty of heat to re-heat it nicely.