Our family name(s) Rayam, Rhem, Ryhm, or Rhim all appear on our family reunion

t-shirts. Why you ask? It's been told that over a century and a half ago several brothers found themselves in a bit of trouble. Something to do with harming or killing a white man in self defense. These brothers had to quickly leave their Carolina homestead and disperse themselves around the country. Texas, Florida, Georgia, Pennsylvania, Puerto Rico and as far as Germany (or so we heard). Supposedly these brothers made a pact to change the spelling of their surname however keeping the same pronunciation (rhymes with Kim) so that they can always find each other. My grandmother is a descendent of Handy Rayam from Bellville, Florida (near the Georgia border). When I was in undergrad at a Pennslyvania University I discovered that another set of Rayams, Rhems, Rhymes, or Rhims was holding a reunion at the Adams Mark in Philadelphia. I attended this reunion but sadly I don't keep in touch with my Philadelphia family. Shortly after I discovered cousins in the north Jersey area. It would be interesting to see how much of the original story stands. Is there any validity in the words that have been passed on almost two hundred years? I believe so, but which ones?