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Glorfindel
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Is there a name for order-preserving functions f where "a <= b if and only if f(a) <= f(b)"?

This is something only slightly stronger than monotonicity. I think that in category theory this would be a fully faithful functor, but I'm not sure if there is a standard name for this in order theory.

For context, I'm working in a theorem prover (Isabelle) and this is a property of the function which converts words to natural numbers (embedding {$0 \ldots 2^{32} - 1$} into $\mathbb{N}$).