growth habit looks to me like some variety of caulerpa macroalgae, probably button/suction cup caulerpa. whether or not you keep it in your tank is up to you -- just keep in mind that caulerpa grows very quickly and can be hard to fully remove once it gets a strong holdfast in rockwork, so you'll need to be aggressive with trimming it back regularly if you want to keep it contained to one spot. some people hate it because it's so stubborn and grows like a weed, but i personally think it looks nice and the fast growth means it can uptake nutrients to outcompete other potential problem algae.