It has also evolved into Peacher and Peecher. I just read a will from 1819 where it was noted that the recording clerk changed William Pitcher's name to Peacher. In my family, sometime in the mid 1800's that spelling evolved into Peecher.
The extended family from across the U.S. (Peachers, Peechers and Pitchers) has a gathering place on Facebook called Peecher's Place. Check it out and join us.