If you click here you will find dozens and dozens of cocktail names...oddly enough, 'highball' isn't among them. The reason for most of the names is lost in time or else has some concocted explanation. For example, it is claimed that the screwdriver got its name among a group of American oilmen working in the Middle East. In the desert, the only handy implement they had to open cans of orange juice to add to their alcohol was - you guessed - a screwdriver. Goodness only knows how the one called 'Sex on the Beach' evolved!
There's an explanation here but I don't find it very convincing.
On American railroads, a ball raised on a pole was a signal that the track ahead was clear. The signal was termed 'a highball'. Since the tracks would normally be cleared to give express trains priority, the trains themselves became known as 'the highball express'.
Personally, I believe that's where the name for the drink came from - its effects being like the trains, speedy, powerful, and direct!
Heathfield's link above illustrates precisely the point I made in my earlier respnse about "concocted" explanations. The plain truth is that no-one knows.