It looks like a pumpkin or squash plant.. If you want it to grow to it's full potential, I'd put it in prepped ground or a way bigger pot.. I've seen squash plants that size transplanted, but you have to be careful with the roots.. Prep the final location first then then try to transplant... I usually wet the soil first before trying to get the plant out. If there is excessive root damage, you'll notice the leaves drooping the next day. Keep the soil moist until it recovers but don't wet the leaves or water too much. If you did the transplant perfectly, the plant will act as if nothing happened...

I don't know how many hours of sunlight squash/pumpkins need but I've grown squash in an opposite scenario, full sun from 11am until 4 pm. It never had full overhead shade, just shadows from one house to the other as the sun moved across the sky... So it may do ok as long as the shade isn't too intense.

Thanks for the help!