Differential privacy basics: Universe \mathcal{X} and database $x$
I am a little late. Your understanding seems correct. $\mathcal{X}=Names \times \{0,1\}$ Where $Names$ are all the possible names that could exist and $x \in \mathbb{N}^{2}$ (Because of $|\mathcal{X}|=2$).
Then you can choose one column and select the histogram of the type you want. Then you can express $x=(x_0,x_1)=(3,3)$ or $x=(x_{ross},...,x_{Rachel})=(1,..,1)$. A you see the first one is more convenient.