Company Names, addresses, dates^1,2:
  Thomas J. Molloy, 1201 K Street SE, Washington DC [saloon] (1900-1905)
  Thomas J. Molloy, 3243 M Street NW, Washington DC [liquor] (1907-1917)

Notes:
Thomas J. Molloy (1873-1940)^2,3 was born in Ireland².
He shows up in the 1897 Washington DC city directory as a bartender¹.
Beginning in 1901, he shows up as a saloon owner in the city directories at 1201 K Street, SE¹. He apparently started as a saloon owner the year before (1900), as he shows up in the 1900 US Census as a saloon owner. His brother Michael J. Molloy is listed in the 1900 Census as living in the same house, with bartender as his occupation, so presumably he worked at his brothers saloon.²

Thomas is listed in the city directory as a saloon owner until 1905, and in 1906 his occupation was listed as "bartender", and his brother Michael was listed as a saloon owner at 332 M Street SW, so maybe their roles were reversed in that year.

Starting in 1907, Thomas was listed under wine-and-liquor dealers, at 3243 M Street NW.
In prior years, Michael McDonnel had been a liquor dealer and saloon owner at that address.

1917 is the last year Molloy shows up as a liquor dealer. In subsequent years he's listed as a hardware dealer at the same address as his liquor busines (3243 M Street NW).

The bottle depicted below presumably held beer, and is the only Molloy beer bottle I know of. There are 3 different Molloy liquor bottles listed in the book.

book # (unlisted) This is a 9.25" clear mouth-blown crown-top bottle, embossed: oval slugplate: T. J. MOLLOY / ('TJM' monogram) / WASH., D.C. heel: THIS BOTTLE NOT TO BE SOLD base: 1