I grew up hearing this great pitcher referred to as Grover Cleveland Alexander. In the last few years, though, every time he’s referred to, he’s referred to as “Pete”…apparently a nickname of some sort. When and why did this change in the reporting occur? Did some grandchild of the late Hall-of-Famer express a preference? I actually spent a while wondering who “Pete” was before I realized he was the guy I’d known as Grover Cleveland Alexander for years.
AFAIK, that was his nickname back then as well. It just carried over into now. BTW, you did know Babe Ruth’s real name was George, didn’t you? 
Nicknames stick. Pete has stuck very well for Alexander.
It’s possible that Grover Cleveland just wanted to be called “Pete” because he was slightly embarrased about his more colorful given name. That, after all, is how Napoleon Lajoie got otherwise known as “Larry.”
The study of baseball history has really improved over the last 10-20 years and I think a lot of common errors are being fixed. Alexander’s common name of “Pete” had just been lost over the years after his career ended because nobody really kept that sort of info in an organized way. There’s other guys like that too; Gavy Cravath’s nickname was misspelled “Gavvy” for about sixty years.