I found a connection with the rivername Rhymni:http://www.mentercaerffili.org/saesneg/gwybodcaerffs.php?hanes=15
"Rhymni – During the Middle Ages the river marked the boundary between the Hundreds of Senghennydd and Gwynllŵg, and between 1536 and 1972 it was the boundary between Glamorgan and Monmouthshire. The name is recorded in a document from the 12th Century as Rymi, Rhymi, and in the tale of Culhwch ac Olwen from the same period there is mention of ‘gast Rhymi’(the Bitch of Rhymi). It is likely that the name comes from the Welsh word rhwmp, meaning ‘auger’, ‘borer’. Sir Ifor Williams said that a rhwmp is a tool used by carpenters to make holes in wood. Gwynedd Pierce comes to the conclusion that the river is so named because of the way it bores its way through the land."