Help! This is from my mother’s funeral six years ago. I don’t know the name and I know it needs a taller planter.
Your plant is called a Dracaena Marginata. It really doesn’t need a different planter, it needs to be pruned. I know this will be difficult, but you need to cut back the thin stalks/stems of the plant one by one. Start by cutting the top 1/2 off of the weakest stem. Two or three new “heads” (groups of leaves) will start to grow right below the cut. New growth with start to grow from the bottom. Once this stalk has started to produce new leaves, cut the next stem. You can read moe about my plant care advice for Dracaena Marginata in the Popular HousePlant section of the website.