Though names starting in Rh aren’t quite as unusual as those starting in Ps and Pt, that’s still not exactly the most common starting syllable. Most of these names are Greek and Welsh.
Female:
Rheia (Latinized Rhea) was the mother of Zeus, Hera, Hestia, Demeter, Hades, and Poseidon. It possibly is derived from the root era (ground) or rheo (to flow).
Rhian means “maiden” in Welsh, from rhiain. Alternate forms are Rhianu and Rhianydd; an elaborated form is Rhianedd (maidens).
Rhiannon is a well-known Welsh name probably derived from Old Celtic Rigantona (great queen). She may have been a Celtic goddess of the Moon and fertility.
Rhoda is an English name derived from the Greek word rhodon (rose). Though it’s found in the Bible, it only came into known English usage in the 17th century.
Rhona is a Scottish name, possibly derived from the Hebridean island Rona. It means “rough island” in Gaelic.
Rhonda either comes from the name of the Rhondda Valley of South Wales (and thus means “noisy”), or was intended to mean “good spear,” from Welsh roots rhon (spear) and da (good).
Rhonwen means “fair hair” or “fair spear” in Welsh, from elements rhon (spear) or rhawn (hair), and gwen (blessed, fair, white). I love this name, and used it on an unplanned secondary character loosely based after a friend from the second of my three high schools.
Rhosyn is a rare, modern Welsh name meaning “rose.”
Rhagnell was a mythical Welsh princess.
Rhanis was one of the sixty Oceanid Nymphs who formed the core of Artemis’s retinue. It means “raindrop” in Ancient Greek.
Rhema is a rare American name, taken from a Greek word meaning “that which is spoken” and referring to the Christian concept rhematos Christou, “the word of Christ.”
Rheta means “speaker” in Greek.
Rhiainfellt means “lightning maiden” in Welsh, from the word rhiain (maiden) and Celtic roots *r–gan– (queen) and mellt (lightning). She was a 7th century queen of Northumbria.
Rhianwen means “fair maiden” or “blessed maiden” in Welsh, from roots rhiain and gwen.
Rhodanthe means “rose flower” in Greek, from roots rhodon and anthos.
Rhodd means “gift” in Welsh.
Rhodope means “rosy-faced, rosy” in Greek, from rhodopos. In Greek mythology, she was the wife of King Haemos of Thrace.
Rhoeo means “stream, flow” in Ancient Greece, from root rhoe. She was impregnated by Apollo, and in a story very similar to that of Danäe and Perseus, her father put her in a chest and sent her out to sea.
Rhadine was the star-crossed lover of Leontichos in Greek mythology. Their love was the subject of a now-lost poem, quoted and given a synopsis by historian Strabo.
Rhoswen means “beautiful rose” in Welsh, from roots rhos and gwen.
Male:
Rheinallt is the Welsh form of Reynold, which is derived from the Germanic Raginald and the roots ragin (advice) and wald (rule).
Rhisiart is the Welsh form of Richard, which means “brave power” and derives from Germanic roots ric (rule, power) and hard (brave, hardy).
Rhett comes from a surname Anglicized from the Dutch de Raedt. Its root is raet (advice, counsel). Anyone who doesn’t live under a rock knows the most famous bearer is Rhett Butler of Gone with the Wind!
Rhodri comes from the Welsh roots rhod (wheel) and rhi (king). A 9th century king had this name.
Rhydderch means “reddish-brown” in Welsh, and is also used as a Welsh form of Roderick (famous power). The latter derives from Germanic roots hrod (fame) and ric (power).
Rhys means “enthusiasm” in Welsh.
Rhadamanthos (Rhadamanthys) may be derived from rhadamnos (branch) and anthos (blossom), or from Rho-t-Amenti (King of Amenti, the realm of the dead), an epithet of the Egyptian god Osiris. In Greek mythology, he was a son of Zeus and Europa, brother of King Minos of Crete, and a judge of the underworld. His name is the origin of the English adjective “rhadamanthine,” inflexibly just or severe.
The Latinized form is Rhadamanthus, and the French form is Rhadamanthe.
Rhain means “stretched-out” or “stiff” in Welsh. This was the name of a son of legendary 5th century King Brychan Brycheiniog, and by a 9th century king of Dyfed.
Rhetorios means “public speaker, orator” in Greek. The Latinized form is Rhetorius. This is obviously the root of “rhetoric.”
Rhidian is possibly a Welsh form of the Irish name Ruadhán, a diminutive of Ruadh (red).
Rhion is both a masculine form of Rhian and a modern form of Ryan (little king).
Rhiwallon is the Welsh form of Old Celtic *Rigovellaunos, which possibly means “lord-ruler” or “most kingly.”
Rhoys is the Welsh form of Roy, which also derives from Ruadh.