Your plant is a Dracaena sanderiana, also known as a Ribbon Dracaena. It is the plant used to make the Lucky Bamboo plant. It will not produce new stems, only get taller. You need to cut the existing stems to get the plant to branch out. This plant likes to be root-bound. Do not move a dracaena sanderiana to a new pot until the roots have filled the existing pot.
Dracaena reflexa is a popular houseplant with origins in Madagascar and other Indian ocean islands. The origin of the plant name comes from the ancient Greek word drakaina or “female dragon,” due to a red gum-like resin in the stems of dracaena that was likened to dragon blood. Centuries ago, this resin was used for toothpaste, dyes, and medicines. Today, it is still used for varnish and photoengraving. The dracaena plant is also known as the Song of India and Pleomele.