The brand name "Hambleton's Hair Stain," along with the picture on the front of the box (below) were registered as trademarks by William H. Hambleton, of Philadelphia in 1897 (TM #30,294). Hambleton claimed to have been using the trade mark since 1855.
I found Job Hambleton listed as a Perfumer in Philadelphia starting in 1868. His primary business location was at 221 Spruce. In 1871, his son, William Harry joined the business and it became known as J. Hambleton & Son. About the same time, they start showing up under Barber's Supples, as well as Perfumery. The last listing I found for the Hambleton business was in 1896. That year the business became known as Hambleton Co., Ltd., and no actual Hambleton family member was listed. Most likely whoever took over the product also registered it immediately. Hambleton's Hair Dye was still listed for sale in the 1901 Morrison & Plummer catalog.