Company Names, addresses, dates:
  G and G Bottling Co, 931 C Street NW, Washington DC (c.1921-1922)¹
  G and G Bottling Co, 209 11th Street NW, Washington DC (1923-c.1925)¹

Notes:
Herbert Guggenheim (b.1885, d.1953)² was in the wholesale liquor business at 1632 14th Street NE from 1907-1911¹. His business was called the "Phoenix Liquor Company". In 1917 he changed to the manufacture of Ginger Ale³.
He ran two companies, the Christo Bottling company and the "G and G bottling Company".
G & G was started by Herbert Guggenheim with a partner named Gunst. Mr. Gunst retired in less than 2 years, and Herbert's brother Sydney Guggenheim (b.1887, d.1928)⁴ took over the duties of Mr Gunst, but Sydney was a paid employee, so Herbert became the sole owner at that time³.
The G&G Bottling company doesn't show up in any of the Washington DC City directories, but I've found ads for G&G Ginger ale in the Washington DC Evening Star and Washington Post Newspapers from 1921 to 1925¹. Some of these ads say if you want to have G & G Ginger Ale delivered direct to your home by the case, phone Main 7637. The wooden crate depicted below is apparently an example of what the case of G&G Ginger Ale was delivered in.
The Aug 16, 1923 Evening Star newspaper reported that G&G was being sued for infringing on the "C&C" trademark of the Cantrell & Cochrane LTD company from Ireland, saying that the trademark was too similar. Guggenheim lost the verdict in November 1925³. I can find no ads for "G and G" after 1925, but there are references to the Guggenheim company after that, which lasted until 1934.

Bottles:

book # 271 This is a 7.5" clear machine-made crown top bottle marked: front: G & G BOTTLING CO / MINIMUM CONTENTS / 8 FLUID OUNCES / WASHINGTON, D.C.

This is a wooden crate with black markings that say: sides: DRINK / G & G / IT SATISFIES ends: G & G BOT. CO. / WASHINGTON / D.C. / PHONE MAIN 7637