According to American Breweries II, a book by Dale P. Van Wieren (East Coast Brewiana Association, 1995), Anchor originally opened in 1895 as Viking Brewing Company located at 18th and Hampshire.  They operated under that name until 1897.

They then opened as Anchor-Shasta Brewing company from 1907-1908.  Then changed to Anchor Brewing Co. from 1908-1920.  Then moved to 1610 Harrison from 1933-1934.

Then moved again to 398 Kansas & 1st St. from 1934-1959.  Then moved again and were located from 1961-1977 at 541 8th St. as Anchor Steam Beer aka Steam Beer Brewing Co.  This is about the time Fritz Maytag bought the struggling brewery.1

They then dropped the last part of the name and were known as Anchor Brewing Co.  Then in 1979 they moved to their present location at 1705 Mariposa and Deharo.  Anchor has not only revived, but they have become one of the most successful breweries in the United States.  And all that great beer is brewed right here in San Francisco.

Here's a picture of Anchor Brewery in 1906 that I took from Anchor's website.

1. All historical information taken from American Breweries II, a book by Dale P. Van Wieren (East Coast Brewiana Association, 1995).