Nice piece of material. The top needs to be reduced down to one of the new shoots, which can be trained upward to build a new apex. Otherwise, you have the branching already to make a good informal upright style.
I agree with Zach, I would cut the trunk and that side branch way back. In fact, I have a similar olive that I've cut way back (two inches about soil line)to make it a shohin (under eight inches). You'll probably find this virtual too extreme but it gives you an idea about what I'm talking about. I think it shows off the trunk more.
I wondered the same. I "googled" it and apparently it's a species known as Osmanthus fragrans a member of the Oleaceae family. So, technically, it is an olive, just not in the genus Olea like most olives I'm familiar with.