Judging by this dictionary entry for hippopotamus, the Romans knew this animal and used the name we currently use in English. This word has an obviously Greek origin: hippos is a horse and potamos is river. But is hippopotamus (or -os in a Greek version) "horse-river" instead of "river-horse"? Surely the word should mean a horse who lives in a river rather than a river full of horses. Or do I make a mistake assuming that in the compound word the main word is the second part and the first part specializes it?
In Latin, Lewis and Short cites instances in Pomponius Mela (AD 45), Pliny (AD 79), and Ammianus Marcellinus (AD 400). In Greek, the LSJ includes references from Dioscorides (AD 90), Galen (AD c. 200), and Damascius (AD c. 538). As you will see you are not the first person to notice its unusual formation.
The rule which is generally observed in Greek (just as in English) is that the attribute precedes the primary noun, i.e. "N1 + N2" = "N2 of the N1." Here are some examples with ἵππος:
- ἱππόδεσμα: bond (i.e. reins) of the horse
- ἱπποδιώκτης: driver of horses
- ἱπποκόσμια: trappings of a horse
Or, in some cases, two nouns together that seem to bear equal weight, as in English "wolf dog":
- ἱππόταυρος: horse bull
- ἱπποκύων: horse dog
(For more examples, see this Greek dictionary search.)
One explanation of this is in footnote 1, pg. 62 of Des origines des sciences naturelles by Dr. Saint-Lager, which contains a lot of useful information in French. Here is my translation of relevant parts:
The word Hippopotamus is improperly constructed, because as a rule in words composed from Greek stems, the principal noun should be placed after the attribute…
As a result, the noun Hippopotamus (river of the horse) should be changed to Potamippos (river horse).
He then includes a very interesting usage note that might explain the reason for this:
Moreover, ancient Greek authors like Herodotus (Histor. II, 71), Aristotle (Hist. anim. II, 1 et 7), Strabo (Geogr. XV, 1 - XVI, 4), Plutarch (Isis et Osiris XXXII et L), [etc.] have always written this in three distinct words: ἵππος ὁ ποτάμιος.
In this instance, ποτάμιος is an adjective in the attributive position, so the phrase literally means "a riverly horse."
Although the footnote goes on to blame the copyists, a likely explanation is that "hippos ho potamios" was judged too long and shortened without proper regard for the usual construction of such compound words. This is certainly not a hard and fast rule, and there are several examples of compounds where the attribute is placed second, as pointed out by @sumelic and @TKR, such as φιλόσοφος (love-wisdom = "lover of wisdom") and ἀξιόλογος (worth-word = "worthy of mention").
Another note is that your suggested combination of potamohippus would be incorrect, since the -os ending would be dropped with a noun starting with a vowel (and no hidden digamma!). One such-formed word is λεύκιππος (leukos + hippos = "riding white horses").