I'm quite sure this can be traced back to his favorite game of "hit the pitch", which like all of Evan's play is full of ritual. Whenever Pat plays hit the pitch with Evan, which is nearly everyday, he offers a fantastic fictional play by play commentary - announcing each pitch, calling strikes, keeping the count and then making up plays to correspond with each hit. Evan loves this, and it really is quite funny. But Evan's favorite part comes before the game can even begin. "Do letters Daddy!". Which is Evan's way of asking for a proper introduction and thus the official start of the game. So, in his best broadcaster persona Pat says something like this:
"Ladies and Gentlemen welcome to Fenway Park, where tonight the Boston Red Sox take on the New York Yankees. Leading off tonight for the Red Sox is Evan Allen Kaplo."
So, given his love of doing "letters" I didn't find it too odd that Evan would make this introduction to random strangers at the park. What I did find odd was his sudden shift to introducing himself as "Ooola". That is a real mystery.