Caulerpa is a genus, with many species. I think yours is C. racemosa, but there are quite a few similar species with very similar characteristics. You can try to search Algaebase to find a possible match but sometimes to be exact we need a microscope and an algae expert. Would just a guess do?
I have that Caulerpa in my tank, and it is a great grower. Does have a tendency to sporulate, though so keep an eye on it? If it starts to go clear, harvest a lot....
I also have the darker type, a Caulerpa also. It is a bit tougher, IMO.