The etymologies of peach and ροδάκινο are quite interesting.
The word peach comes from Middle English peche, from Old French pesche (French: pêche), from Medieval Latin pesca, from Vulgar Latin pessica, from Classical Latin persica, from malum persicum, from Ancient Greek μῆλον περσικόν (“Persian apple”).
The word ροδάκινο comes from medieval Greek ῥοδάκινον/ῥωδάκινον, from later Greek δοράκινον/δωράκινον from the latin duracinum duracinus (durus + acinus, durus meaning hard and acinus meaning fruit.)
So the English word originates from Greek and the Greek one originates from Latin. xD
Modifiers in Greek are quite complicated and can’t be easily explained in a post. In this instance, as Dimitra says, both “χυμός ροδάκινο” and “χυμός ροδάκινου” can be correctly used indeed. “Χυμός ροδάκινο” is an adjunct noun where the modifier noun is in the same case as the noun it specifies. This form is used because the modifier gives the noun a permanent quality, and describes one specific thing. The emphasis is on the end product as a whole, rather than the material from which is made, and that’s why this is the most used form in this example. On the other hand, “χυμός ροδάκινου” has the modifier in genitive case in order to specify the material from which the product is made. In this example it’s uncommon, but in a similar situation it’s not – for example you would probably say “χυμός πορτοκάλι” when you order an orange juice, but in a baking recipe it’s most likely that it would be referred as “χυμός πορτοκαλιού”.
Please notice that not in all instances are both forms correct, and sometimes depending on the form you use, you are talking about different things. For example, “ένα φλιτζάνι τσάι” is a cup of tea, but “ένα φλιτζάνι τσαγιού” is a teacup.
Very good explanation! I doubt that it is correct to use it in the form χυμός ροδάκινο. The language used in everyday life does not always follow the rules of the Greek language . Should we correct it? Yes and no. Language is an alive organization and it changes by the time. I insist on the proper use of modifiers: Genitive case is better, χυμός ροδάκινου. Genitive case exists for that reason, as you described, otherwise why should we use it? But we don't know the future. In a Greek language of the future it is possible we will not have any case. But we have now!