The name refers to the roach (Rutilus rutilus), a common European fresh water fish. It has nothing to do with the cockroach, and nothing directly to do with the either the French given name "Roche" or the character Vernon Roche. Though the English term for the fish ("roach") does in fact share its origin with "Roche": both terms come from the French word for "rock".
It's worth noting that the original name for the horse in Polish is "Płotka", a diminutive form of the word "Płoć" (meaning "roach"). Diminutives are endearing in Polish, so a more direct translation would have been something along the lines of "Roachy" or "Roachie".
Moreover, the Polish word is female gendered which corresponds with Geralt's preference for mares - it would be odd for a stallion to be called "Płotka". The tender tone as well as the gender of the name is lost in the translation.
However, "Płotka" has another meaning which is "small fry". In the Polish version of the third game, this is brought up during Broken Flowers if Geralt beats Morvran Voorhis in a race, who will praise him by saying "Impressive rider skills from someone for whom every horse is a small fry." In this meaning the name becomes gender neutral, thus can be used for a stallion as well.