Hi Aaron,

Your plant is called a Dracaena TriColor. It is a stalk plant so it is normal for the bottom leaves to drop off as new leaves appear at the top. Dracaena TriColor houseplants get brown tips when they are over-fed, or getting water that has too much fluoride, chlorine, or salt in it. The Dracaena TriColor is a close relative of the Dracaena Marginata Plant. You can read my care tips for a Dracaena Marginata houseplant in the Popular HousePlant section of the website. The only difference is that a TriColor Marginata needs more light to keep its color.

https://www.houseplant411.com/houseplant/dracaena-marginata-plant-care

Here is a picture of a full grown Dracaena Tri-Color.

Dracaena marginata Tricolor