The form rhaes in the Etymologies is a misreading according to VT/46:10
Noldorin
rhom
noun. horn, trumpet
rhom
noun. horn, trumpet
rhomru
noun. sound of horns
rhomru
noun. sound of horns
rhimbron
masculine name. Rhimbron
nella-
verb. to sound (of bells)
rhas
noun. horn (especially on living animal, but also applied to mountains)
rhasg
noun. horn (especially on living animal, but also applied to mountains)
rhasg
noun. horn
rhû
noun. loud-sound, trumpet-sound
tarag
noun. horn
tarag
noun. steep mountain peak
tild
noun. horn, point
till
noun. horn, point
till
noun. horn
Earlier names for S. Rúmil in Lord of the Rings drafts from the 1940s (TI/236). The meaning of this name is unclear.