Not really a stamp related query, but I cannot resist poking at it a bit.
Identifying photographic studios and photographers is still best done by looking at the specific locale. National level searching is still pretty rudimentary. Your card appears to me to date from back around the turn of the century - which is actually good. It doesn't give a specific address, though, which many did as a form of advertising. If it had been posted, the cancel would give us a date, too, but we press onward.
Nationally, there is Langdon's List of 19th and early 20th century photographers https://www.langdonroad.com
Looking for S. Kaufman gives two hits.
Kaufman, Saml, New York, NY
Kaufman, Samuel, New York, NY
Kaufman, Sol, New York, NY
Kaufman, Solomon, New York, NY
But Langdon goes no further. You have to go local.
There is a great searchable website for early New Jersey photographers, for instance, but for a lot of other areas, you have to resort to a book, or search a city directory, to identify turn of the century photographers. Fortunately, many of these city directories are now being scanned and are searchable (or alphabetically browsable) at HathiTrust, a cooperative venture of our largest university research libraries, or through Google. They are not generally available full-text online for after 1923 due to copyright, however.
So - New York:
It happens I have done a fair amount of work in New York City directories chasing my own and my wife's relatives. So finding the following did not take long.
In this case, I believe your S. Kaufman is either:
a Samuel Kaufman, who ran a photographic studio at 1398 3rd Avenue New York City as listed in the 1915 Polk's NYC Directory (p.1019).
a Sol[omon] Kaufman whose studio was at 287 E. Houston St. https://babel.hathitrust.org/cgi/pt...919&size=150
I think the odds are that it is Samuel Kaufman. He ran what was likely a larger firm, as evidenced by his being listed in the Trow business directory for New York (1912, p. 443) d.b.a. "Kaufman's Photo Studio.". https://babel.hathitrust.org/cgi/pt...=1up&seq=483