I need another ID please

[commod0re]

I was thinking probably not cup coral because OP said it moved on its own… can they move????

 

[Fish Fan]

It looks like some kind of small anemone to me, perhaps a majano. Either way, it looks like it's growing up under a frag plug, and for that reason it's likely a pest 'nem and I would get rid of it, whatever it is