I was given this "stick" about 10 years ago and told to stick it in the dirt. I did and now I have this wonderful plant that I know absolutely nothing about.
plumera is right,they like to sell those" sticks" at amusement parks around here.they are native to hawaii and are not cold tolerent above zone 10 at best,i am in orlando, florida and i wont grow them in my yard becuase the winter here,even though mild,will kill them.so if you are not in exteme southern U.S. bring it in when waether drops below 40-45 degrees.they are beautiful plants especially if you can get them to bloom
The plumeria shown,( also called frangipani ) is the plant from which the flowers come that are used to make the "Hawaiin Lei". Suggest you keep it warm and give it LOTS of light. It can be of a large variety of colors.
Probably Plumeria rubra. If 10(!) years old has been growing at a snail's pace, try a bigger pot - and looking up cultural requirements, trying to improve conditions for it in other ways.
As an addendum, I would add that the soil I see in the pot is almost 'non-existent'. Don't know where you live, but I too have a plumeria 10 years old, in the ground, that is 12 feet tall and 15 feet across. Each spring it will have several hundred bloom stems. It too, started as a stick, as most frangipanis do, although they start quite easily from seeds.
Their 2 posts are from over a year ago, so we are probably talking to ourselves and whoever else might be interested.