Looks very much like 'pulsing sinularia'. A lot of people call any larger octocoral a Leather, though I wouldnt personally use that term to describe what you have.
They do shed, but not very often. Can grow exceptionally large, and pretty quickly. I have two big colonies of it in my tank that at one point would have been over 4 feet across put together, all from a single 2" branch. Good stuff!