Beryl was in the SSA top 1,000 in 1880, when it was #518, and stayed on the list until 1957, when it last appeared at #913 before disappearing entirely. It was most popular in 1920, when it reached #372 (the modern day equivalent would be Kenzie) and was a pretty steady presence in the 400-600 range for most of its run, until the early '50s, when it started to fall.
Aquamarines and emeralds contain beryllium — a deep-blue version of aquamarine is called Maxixe. The Middle English and old French versions of emerald would make beautiful, very unusual choices — they are Emeraude and Ésmeraude, respectively.
The English word "brilliance," is derived from beryl, and some names with shiny meanings include Cassandra, which comes from Greek elements and means "to shine upon man" — Castor comes from the same roots. The "-dra" ending of Chandra puts me off, but it means "moon" in Sanskrit, and is derived from the element Chand, meaning "to shine," which I find much more intriguing on its own. Dai, a Welsh diminutive of David, also means "to shine."
Unisex Hebrew name Zohar means "light," or "brilliance," and has great variants, including Zahara, Zaahir and Zaahira. Arabic name Sana means "radiance" and currently cracks the French top 200. One of the three Graces of Greek mythology was named Phaenna, which means "shining." Russian form Faina is also nice. Another mythological name is Taliesin, which means "shining brow," and was the name of a wizard-prophet of Welsh lore.
One can also find inspiration in the color of the gemstones themselves. Irish male name Odhrán (pronounced "O-rawn") means "little pale green one," and variants Orin and Odran are quite handsome. Even the word "green" itself might offer some name possibilities when translated, if you don't mind venturing into "naive" or "immature" territory — like Éretlen (Hungarian), Vert or Verte (French), Verdura or Novellino (Italian) and Midori (Japanese).