Completeness from an example
Yes, the relation $B$ over $X$ is not complete since $3 \in X$ but $(3,3) \notin B$. 

The variables $x$ and $y$ in the completeness definition "$\forall x,y \in X, xBy \lor yBx$" are treated as placeholders and thus are not necessarily distinct. In fact, completeness implies reflexivity when you let $y = x$ in the definition.