The botanical name is H. rosa-sinensis followed by whatever the cultivar name is. It is a borderline zone 9 plant, so you will definitely need to keep it potted and bring it in for the winter.

Whether you need to repot it would depend on whether it looks rootbound or not.

If you do decide to pot up, only go one size up. Maybe to a 10" pot (check the bottom to see if the plant has roots coming out, or carefully tilt the plant out to check the rootball).

These can be kept outside all summer in a sunny location, although I noticed they may do better with some afternoon shade. They can be overwintered inside. When inside, you could choose to keep it under alot of bright light and in warmth and it may continue to flower all winter (albeit, much less). Alternately, you can keep it in a cool bright location and let it rest. In either case, don't water it much (perhaps once every couple weeks while inside). Also make sure that you try to provide alot of humidity for it as it can become a spider mite magnet. Also note that any change in its conditions (location, amount of light, water, and temperature), will often cause some of the leaves to suddenly turn yellow and drop off. Don't panic and just ignore it. Once you stablize the new site and your watering practices, it'll regrow the leaves and they will become accustomed to that new regime. When you move it out in summer, it'll do the same thing, but by then, you'll know why. ;-)

One thing to be careful of is since yours is grafted, sometimes the grafts can snap off way to easily.

Nowadays, I give mine a slow-release all-purpose balanced fertilizer and will occassionally give it some Ironite and epsom salts (1tbsp per gallon of water).

Good luck. I bet it's beautiful!