It does look a lot like that aucuba japonica, but this is a some type of tropical and the leaf edges are smooth instead of jagged. My picture doesn't show that very well at all - I just got the polka-dots! :o)
I believe it is some kind of croton/Codiaeum. but for the life of me I cannot find it online. I just keep finding the bigger one, But I strongly believe it's what it is. I wanted to pick it up myself a few times, but I really don't have the right enviornment for them. Even though I have the bigger one. Well I am babbling, so I'll move on now. I hope I'm right...lol It will make my day :) being that I am fairly new to all this.
(forgot to put my name :O) )
That thar's a Codiaeum variegatum, or croton, allright. They grow into humongous shrubs in zone 10, outside. Variegation changes with respect to light exposure, and the shape and size of leaves varies from long and narrow to more rounded to trilobed. There are countless color variations too, with spots and splotches yellow, orange, red... They're a wonderful color addition to the home.
They like to have their soil a little on the moist side. Watch out for spider mites, which love them. (little webbies at the leaf axials, and a dirty appearance on the underside of the leaves). Keep those at bay with a soap spray. The plants like a daily water spritz if you've time. HTH, perL :)
To be very precise, you have a codiaeum variegatum pictum 'Aucubaefolium'. It is commonmly called aucuuba leaf croton because of its physical resemblance to a miniature aucuba (Right-on , Larkie!). It has the same cultural requirements as other crotons, but this one can tolerate dryness better than other crotons.