Yes that is a branching, not common but I've seen them around. I have 13 of goniopora corals from many kinds in my 65 gal tank and have had them there for a good year now. Care isn't much different from other LPS, but I would feed them. I've read tons from experts saying feeding will assure their success, but also have seen people neglect that and also keep that coral with success.
Gonioporas have become my favorite coral, and I think you gotta find their sweet spot in order for them to do well.
Find a place where there is medium light, medium flow and direct feed the tank maybe 1-2 week with zooplankton and phytoplankton. I notice some of them react to food, while others don't. There are some types that are really hard to keep, while others are easy.
The one you have seem to be Australian, since the polyps look smaller, with more tentacles. I have a piece similar to yours but orange and it does very well.
There are tons of food for these corals these days, you can chose the one you have better availability in your city stores.
Good luck and congrats on the piece!