Welcome to Over50sForum! The site for people over 50 to chat, make friends, discuss, share, and generally be part of something that's fun and friendly :)
My plant guru a.k.a. Rosemary, says it's a "Draceana Marginata" (Dragon Tree) and needs a little watering when the top inch of soil is dry, but it will lose a few leaves over the winter anyway, just a natural process.