Company Names, addresses, dates:
  Fuller Pharmacy Co., 125 N. Union St., Danville VA
  Beck & Fuller, 125 N. Union St., Danville VA (c.1920s)

Notes:
I can't find the Fuller Pharmacy in any of the Danville city directories, but the Beck & Fuller drug store is listed in the 1921 directory.
Other drug stores at that same address (125 N Union St) include the James C. McFall drugstore up to 1908, and Blankenship's Pharmacy starting in 1927. So it seems likely that the Fuller Pharmacy was in business somewhere in between those 2 years (1909-1926).¹
The fact that the phone number on the bottle below is just "2" would indicate that this drugstore was around when Danville first got telephones installed.
Frank M. Fuller was listed as a clerk at Beck & Fuller in 1921. He's also listed as a druggist at other Danville drugstores in subsequent years, so I suspect he's the guy who the Fuller Pharmacy was named after.
More information about Danville drug stores is available at rdricketts blog.

Bottles:

Clear 5.9" (4 oz) bottle embossed: vertical on front: PHONE 2 / FULLER PHARMACY CO. / DRUGS AND SEEDS / 125 N. UNION ST. DANVILLE horizontal on rear in script: Fuller's base: C L G CO / A