The first thing I thought of was also order embedding (like Bjørn), but one can also say that $f$ preserves and reflects the order. That way, you understand even if you don't know what an order embedding is.

The first thing I thought of was also order embedding (like Bjørn), but one can also say that $f$ preserves and reflects the order. That way, you understand even if you don't know what an order embedding is. Folks sometimes write that $f$ is a strong order homomorphism in this situation.