The name can be arbitrary, as long as it's unambiguous. By the way, here's what mathematica says when I copy paste that and enter x∘y: SmallCircle[x,y]

Also fun:

    In[3]:= SpokenString[x\[SmallCircle]y]
    Out[3]= "SmallCircle of x and y"

Which can be turned in to sound:

    Speak[x\[SmallCircle]y]