Aloha! Thevetia peruviana is the actual name of this plant. It's most common common-names are Luckynut and Yellow-oleander, but it is sometimes also called Be-Still Tree.

Deer are really hard to predict. Their behavior often varies considerably with species, geographical location, and current conditions (availability of food, etc). Deer are often described as willing to eat almost anything if they are hungry. The only way I know of to get an idea of whether they will bother the plant in the future is to watch and see what happens. Your local extension agent might be able to give you a better guess, factoring in local information/knowledge. But, at best, you'd only get a better idea of what's typical, and not what's necessarily going to happen. If the plant is part of your landscape and you don't want it damaged, I'd recommend either providing some type of protection or repellant. Your local extension agent might be able to provide some good ideas about that too.

Interesting. This is what we call Mexican Oleander here in Texas. I'm surprised that deer would eat it.