Looks like a Dracaena, massangeana or fragrans. This discussion may be relevant. Different plant, but almost identical in regard to pruning/propagation.

Ficus benjamina You can find plenty information about them on gardenweb.

I think its a Ti-plant (Cordyline terminalis) here are some pics in the link Here is a link that might be useful: Cordyline terminalis

It's on most of the lists of plants that can be toxic to cats and dogs. And if it's not on a list, it should be. Don't you wish that there was a way that these people who sell plants be responsible for proper labels? We certainly expect that from reputable garden centers.