It is Neomeris sp.
(Hobbyists typically run into either N. annulata or N. vanbosseae)
A macroalga, it is sometimes referred to as Mermen's fingers.
The whitish material about the base is calcareous, and the alga collects this from the water. Individuals can grow up to 2" or more in length.
If you see it multiplying too rapidly, let us know.
Usually it doesn't misbehave, and can be quite attractive in small clumps.