Definitely unique! I'd take the rocks that are resting on the side glass and move them - trust me, when the coralline starts to spread you'll rue the day you leaned them on the glass.
In regards to the coral it does look a little like a goniopora - however, I have a quick question: when it's retracted, is the base rounded or flat?
Grab some snails to take care of the green algae and test your nitrates and report back. A few water changes might help clear it up.
Also - you're gonna want to keep your calcium and alkalinity in check to encourage coralline.