Name for this logic operation
No, there is no name for that custom logic operation.

You'll have to implement the function below in whatever environment you are working in. 

\$
  f(a,b,c)=\begin{cases}
  \displaystyle 0 &amp; ,\text{when } abc=1 \\
  \displaystyle \text{xor}(a,b,c) &amp; ,\text{otherwise} &amp;
\end{cases}\$

Or, if you don't want to deal with cases, this function gives the same answer:

\$
  f(a,b,c)=\text{xor}(a,b,c)(1-abc)
\$