Rahmi is of Turkish origin, meaning 'merciful' in Arabic. It's composed of two elements: rah, 'compassion', and mi, a suffix denoting 'giving'. This name is often associated with Rahmi M. Koç, the renowned Turkish industrialist and philanthropist.
Rahmi is quite an uncommon name, with only 10 individuals born in those two years combined. It seems to have seen a resurgence recently, however, as both years had equal numbers of newborns bearing this name.