I believe what you have is a Dracaena marginata.

It is definitely in shock and the most important thing to due is not to panic.

First make sure that you didn’t plant it too deep. When you repotted the Dracaena it should have been at the same level as before — the top of the original root ball should still be the top in the new pot — any extra soil should have only been added underneath the original root ball and around the sides to fill in the space between the new pot and the original root ball. When you repot any plant you saturate the soil immediately after you pot it and then follow normally watering practices.

Once you have checked the soil and made any necessary changes, it becomes a wait and see approach. Within a week the plant should start to recover from the transplant shock as long as you treat it the way you did before. Most people want to water more or fertilize a plant when it is going through transplant shock this is not a good idea. Instead pretend nothing has change and treat the plant the way you did before it was transplanted. This gives the plant time to recover in an atmosphere in which it is accustomed.

Dracaena marginata is a pretty resilient plant and is one of the most frequently used houseplants. In fact, Dracaena marginata makes a great house warming gift.