I would almost guarantee its a malu. And it looks like one, too.
Although they are common, they are very difficult to keep alive for the first few month. Fortunately, your anemone looks like it hasn't bleached or lost its zoox algae. In fact, your anemone looks really good and I think it has a promising future. Usually they have pink or purple tips but not always.
As for care, it is a sebae anemone so it tends to prefer rubbley bottoms. If that pic you took is from your own tank, I would say the substrate looks good for the anemone. You can try to feed it pieces of shrimp, squid, or some krill. I haven't had success with fish but it's all in the anemone's preference. Yours might like silversides. Try feedings 2 to 3 times a week. If your lighting is good, you can cut this back to once every week or two.
These anemones do require quite a bit of light. I would suggest PC as an absolute minimum but you would be best to use metal halide for any host anemone. If you are upgrading lighting, get MH.
One regular fish found with this anemone is the sebae clown. These aren't particulary common (nor are they rare). But many anemone fishes like the sebae anemone.
Heteractis malu