Montgomery County, Alabama (This county was not named for Richard Montgomery, but for another general, Lemuel P. Montgomery; oddly, the city of Montgomery, Alabama in it was named for Richard Montgomery.)
Montgomery County, Pennsylvania (there is some question as to whether this one was named for Richard Montgomery. It seems to be the case, but it is uncertain.)
Montgomery County, Tennessee (This county was not named for Richard Montgomery, but for John Montgomery, a local settler)
Montgomery County, Texas (This county was not named for Richard Montgomery, but (indirectly) for Andrew Montgomery, a local settler)