Like a correct person, I have always pronounced the name "Reese's" as "REE-says." Everyone I knew did this. I never had cause to doubt it.
Then one day, about five years ago, we were driving through Romney, West Virginia, and we stopped at a Dairy Queen. I ordered a Reese's Blizzard and the woman had a hard time understanding me. Then she said, "Oh, REE-SEES."
I chalked it up to the eccentricities of West Virginians. But later we moved to western Ohio and many non-idiot people we met there also said the name as "REE-SEES."
Here's the deal, though: this isn't just a matter of "tomato/tomahto." Because we know how to pronounce the word "pieces". So even if we don't know if H.B. Reese pronounced his name as "REES" or as "REES-EEE," we can be sure that no company on Earth would develop a candy intended to be called "REE-SEES Pieces."