Company Names, addresses, dates:
  Hogshead Brothers & Co Corner Main & Augusta Streets, Staunton VA (1900-1903) ^1,2,3
  Harry Hogshead, Waynesboro VA (1903-1905) ^2,7
  Harry Hogshead, Western State Hospital, Staunton VA (1906-1908) ^8,9
  Harry Hogshead, Pineville Kentucky (1908-ca.1912) ^9,10
  Harry Hogshead Druggist, Western State Hospital, Staunton VA (1912) ¹¹
  Virginia Pharmacy (Harry Hogshead prop.), under Hotel Virginia, Staunton VA (1912-1921) ^3,11
  Harry Hogshead Pharmacy, S New cor Kalorama, Staunton VA (ca.1918-ca.1924) ^3,12
  Harry Hogshead Pharmacy, 101 S New Street, Staunton VA (ca.1927-ca.1931) ³
  Harry Hogshead, Fishersville VA (dates unknown)

Notes:
Harry Hogshead (1878-1961)⁴ became a registered pharmacist in 1899.⁵
In 1900, he joined his brother Thomas Hogshead, with the firm being called Hogshead Brothers & Co.¹
That lasted until 1903, when Harry bought out a drug store in nearby Waynesboro VA, and went into business for himself.²
In 1904, Harry was thrown from a horse and broke his collar bone⁶.
In 1905 he put his drug store up for sale so he could recover from an accident⁷. I don't know if it was the broken collarbone from 1904, or another one.
By the end of 1906, he had become the pharmacist for the Western State Hospital in Staunton⁸. Wikipedia says the Western State Hospital was a hospital for the mentally ill.
In 1908, Harry resigned as the W.S. Hospital druggist⁹.
He then moved to Pineville Kentucky to engage in the drug business there¹⁰.

For whatever reason, that didn't last long, as by 1912 he had returned to the Western State Hospital in Staunton, and also took over an existing pharmacy in Staunton called the "Virginia Pharmacy"¹¹.
Sometime after that, he was running his own drug store at the corner of South New Street in Staunton. That is shown on his WW-I draft card, dated 10-Sep-1918¹², as well as in the Staunton city directories³.
He continued to run his own drug store until at least 19xx¹², at or near the corner of S New Street and Kaloram Avenue. There is some overlap in city directories that list the "Harry Hogshead Pharmacy" and the "Virginia Pharmacy, Harry Hogshead proprietor" between 1916 and 1921, so I suspect these were 2 different names for the same drug store³.

The 1934 Staunton City Directory listed Harry as a druggist at the Western State Hospital. His circa-1942 WW-II draft card also listed him working there. But his Virginia State Death Certificate listed him as a self-employed Pharmacist, so I'm not sure if he owned a drug store at the Western State Hospital, or if he worked there and also owned a separate drug store in his later years.

I was unable to find any indication that he owned a drugstore at Fishersville VA, other than the label on the bottle shown below. Fishersville is very close to both Staunton & Waynesboro VA. I've seen another bottle with a label from Hogshead in Fishersville, and it was also a machine-made screw-top bottle, like the one below. These bottles are likely from sometime after 1930, possibly much later.


Bottles:

This is a clear 2.75" machine-made screw-top bottle with a label. Front & back views shown. The label says: label: Harry Hogshead's / FIRST AID / ... PRICE 15 CENTS / 1/2 FLUID OUNCE / Manufactured and Gauranteed by / HARRY HOGSHEAD / FISHERSVILLE - - - - VIRGINIA