What should I call this commutative monoid of order three?

Question

I'm looking for a name for the monoid given by the following table:

$$ \begin{array}{c|ccc}&1&a&b\\ \hline 1&1&a&b\\ a&a&1&b\\ b&b&b&b \end{array} $$

Is there a name that would be understandable to an undergraduate student who hasn't read anything about semigroups but has had a first course in algebra and knows what a semigroup/monoid is? What name would it be good to go under in a list of order-three semigroups?

Answer 1

Call it : $(\mathbb{Z}/3\mathbb{Z},*)$

Answer 2

In computer science I would call it $\mathbb{Z}_2$ with errors, i.e. $ \langle \{0,1,\bot\},+,0\rangle $. In math I would follow hassan's idea.