Suppose $X$ and $Y$ are jointly distributed real-valued random variables and for all outcomes $\omega_1$, $\omega_2$, we have $$ X(\omega_1)\le X(\omega_2)\quad\Longrightarrow\quad Y(\omega_1)\le Y(\omega_2). $$

**Edit**: As Louigi Addario-Berry's answer below shows, it may be better to consider the following variation:
$$
X(\omega_1)< X(\omega_2)\quad\Longrightarrow\quad Y(\omega_1)\le Y(\omega_2).
$$

Does this property have a name?