We have Professors Oak, Elm, Birch, Sycamore, etc, in the games. We also have Professor Ivy, etc.---in the anime.
There's no real reason to why they're all named like this, but rather they primarily do it to just follow a fun naming scheme. Naming schemes are common in a lot of media. The most common use of this is the use of the 7 Deadly Sins as names, found in several pieces of entertainment. You never know though, Game Freak might run out of trees eventually!