This is a simple terminology question, but I don't know what to search for.
Suppose $(X,G)$ is a (topological invertible) flow, that is, a dynamical system consisting of a topological space $X$ and a group $G$ that is equipped with an action on $X$ by homeomorphisms. Often one focuses on compact minimal flows, meaning that $X$ is compact and there is no proper nonempty closed $G$-invariant subset of $X$. A factor of $(X,G)$ is a flow $(Y,G)$ admitting a quotient map $\pi: X \rightarrow Y$ such that $g.\pi(x) = \pi(g.x)$ for all $g \in G$ and $x \in X$. Compact minimal flows can certainly have nontrivial factors in general: for instance, if you start with the circle group acting on itself, then for every natural number $n$ there is an $n$-fold covering map $\pi: X \rightarrow Y$, where $Y$ is also a circle but now $g \in G$ acts as $g^n$ on $Y$.
Now suppose $(X,G)$ is such that, whenever $\pi: X \rightarrow Y$ is a factor map onto a flow $(Y,G)$, then either $\pi(X)$ is a single point or $\pi$ is injective. Is there a standard name for this or something similar? My first thought is to call it 'topologically primitive' by analogy with primitive permutation groups, but probably this term is already in use.