There is only one village named
Penn Yan.

But wait!

In Bainbridge township, Berrien County, Michigan, there is a section that was called "Penn Yan" -
complete with a "Penn Yan School" and a "Penn Yan Cemetery"!

In the 1800s, several families moved from the Penn Yan, NY area to Bainbridge township, Berrien County, Michigan, which is located about ten miles east of Benton Harbor and Lake Michigan.
So many Penn Yan-ers relocated there that the area became known as Penn Yan.

Penn Yan School photo HERE
Penn Yan Cemetery photo HERE
Penn Yan Cemetery burial records HERE

The second "Penn Yan Cemetery" website includes a comprehensive record of burials in the cemetery from the years 1837 to 2003 with names, dates and notes. It also includes this short description of the cemetery:

"Located on Bainbridge Center Road, one half mile south of Napier Avenue on the west side of the road, or one half mile north of Meadowbrook Road. A gated fence surrounds the cemetery. This cemetery began as the burial ground for people living in the Penn Yan settlement (the southwest portion of Bainbridge Township"

Further information:

The History of Berrien and Van Buren Counties, Michigan was published in 1880 in Philadelphia by D. W. Ensign & Co. Under the section for Bainbridge Township of Berrien County you can read on page 217: "The Penn Yan Settlement. The southwestern portion of Bainbridge is popularly known as Penn Yan, a name given to it by Isaac Youngs after the Brants located there. The first settlement in this part was made by the Brant family, of Wayne Co., N.Y. Simeon Brant with his wife and four children-Nathaniel, John, Daniel, and Augustus-came to Michigan in 1836, and made settlement upon section 31 in Bainbridge township, where the elder Brant had, previous to his coming hither, bought 80 acres of land of Darius Clark. At this time the southern tier of sections in Bainbridge was an unbroken wilderness, into which Brant was the first to venture as a settler. With the aid of his boys, he chopped out a road to his place, put up a cabin, and made a clearing."